The pronunciation of gross seems to be related to French pronunciation
The word "gross" comes from the French adjective gros, which is spelled with a double S in its feminine form grosse. I have the impression that grosse has a somewhat "exceptional" pronunciation already in French: rather than being pronounced with [ɔ], it is often pronounced with [o], which is a violation of the French "loi de position". (See post #52, by merquiades (Apr 30, 2014) in the following Word Reference thread: O-like vowels (RP English). Some modern French accents do have [ɔ] in grosse ("Combien d'accents en français?
Focus sur la France, la Belgique et la Suisse").) I would guess that the French pronunciation of grosse with [o] is related to the English pronunciation with the GOAT vowel (i.e, the vowel phoneme found in the word "goat", also called the "long o" sound, transcribed in IPA as /əʊ/ for British English or as /oʊ/ or /o/ for American English).
Although I've only ever heard the word pronounced with the GOAT vowel, it seems that some English speakers may use the LOT vowel (or perhaps the CLOTH vowel, in accents where CLOTH=THOUGHT) in the word gross. Specifically, this pronunciation appears to be associated with Scotland. John Wells wrote a blog post "a gross violation?" that says that the English journalist Simon Hoggart criticized the Scottish politician Gordon Brown for allegedly using a pronunciation like /grɒs/ (I haven't been able to find any audio samples that would allow me to confirm that this is a feature of Brown's pronunciation), and we find a comment below by The Blob5, June 2012 at 14:53, that says "Gross-like-floss is a common pronunciation among the older generations in Scotland." I also found another post, in the WordReference thread "dross: pronunciation", that says "In Scotland, there is a prevalent pronunciation of 'gross' to rhyme with 'loss'" (wandle, Jul 28, 2012 #10), and this pronunciation is mentioned in John Walker's Critical Pronunciation Dictionary of 1791:
This word is irregular from a vanity of imitating the French. In Scotland they pronounce this word regularly so as to rhyme with moss. Pope also rhymes it with this word.
"Shall only man be taken in the gross?
"Grant but as many forts of mind as moss."
This, however, must be looked upon as a poetical license; for the sound is now irrevocably fixed as it is marked, rhyming with jocose, verbose, &c.
Other words like gross?
The Wells blog post says that gross (and related words like engross) are the only words spelled with "oss" and pronounced with the GOAT vowel in a typical British English accent. The linked WordReference thread indicates that least a few American English speakers apparently grew up pronouncing "dross" with the GOAT vowel, but it's unclear if this is anything more than just a sporadic mispronunciation used by people who saw the word in writing before hearing it and guessed at the pronunciation. (E.g. compare "OAR-y" for "awry" and "MIZZ-uld" for "misled", which are both attested as pronunciations used by some native speakers, but are definitely not considered correct in any accent.)
Other people have brought up cases of diphthongs before consonant clusters, like pint, but technically these are not an exception to the rule that you mentioned, which deals with a "repeated consonant in spelling". In "pint", no consonant letter is repeated.
In fact, there are very few true exceptions to the rule as you have stated it.
Words ending in "oll"
I only know of one major class of exceptions: words ending in "oll" like the word "poll" mentioned in Astralbee's answer. Some have the LOT vowel (or in many or all American English accents, the CLOTH/THOUGHT vowel), like doll, but many have the GOAT vowel, like roll, scroll, troll, stroll, poll, toll, droll.
But even these words may not necessarily be exceptions, because not all speakers pronounce the GOAT vowel as an closing diphthong in this context. Some speakers, like me, have an allophonic realization of the GOAT vowel in this context that sounds closer to [oɫ] or [oə̯ɫ] than to [oʊɫ]. (For example, I hear a difference between my pronunciation of slowly, which I would transcribe as [ˈsloʊli], and my pronunciation of holy, which I would transcribe as [hoɫi] or [hoə̯ɫi]. I pronounce the vowel in words like scroll like the vowel in the word holy, not like the vowel in the word slowly.)
Alternatively, in certain accents, the distinction between the GOAT vowel and some other back vowel phoneme may be reduced or eliminated by phenomena like l-vocalization, or mergers of certain vowels preceding /l/—the Wikipedia article on "English-language vowel changes before historic /l/" mentions some relevant mergers that occur for some speakers.
Bass in the sense "low" (not the fish)
Another freak exception like gross is the word bass in the sense "deep/low in the musical scale" (the explanation for that is given in the answer to the following EL&U question: Why does “bass” sound like “base”?). I don't know of any other exceptions beyond these, as long as we're talking about the pronunciation of single vowel letters rather than digraphs, and restricting the discussion to stressed vowels.
Vowel digraphs before double consonants (uncommon)
Vowel digraphs occur fairly infrequently before double consonants, but when they do it's not unlikely that the word is pronounced with a diphthong (if the vowel is stressed): e.g. the word surveillance has a "long a" sound in the stressed second syllable, and when renaissance is pronounced with stress on the second syllable, that syllable has a "long a" sound (in American English, it can be pronounced with stress on the first, in which case the second syllable has a reduced vowel sound).
Unstressed vowels in some words (not worth learning as an exception)
Vowels in pre-tonic word-initial syllables are sometimes pronounced as "long", even when there is a following double consonant, but this is never necessary and in some cases I have the impression that it can even be stigmatized (specifically, I think I've seen criticism of the pronunciation of the word dissect with a "long i" in the first syllable) so I wouldn't recommend trying to learn these words as a class of exceptions. I just thought I should mention them for completeness. This phenomenon can occur with the letter "o", as in "official", or "e", as in "effective". More commonly, "official" and "effective" are pronounced with reduced vowels in their first syllables.