I can't believe [(that) you remembered that blue is my absolute favorite color].
The reason is that the bracketed expression is a separate subordinate clause that is embedded within the larger (matrix) clause. Note that the subordinate clause has its own subject, you, and its own predicate, remembered that blue is my absolute favorite color. Grammatically, the clause subordinator "that" can be optionally added, as shown.
The subordinate clause here is called a declarative content clause, and it is functioning as complement of the verb believe. It is not the object of believe, since objects are (almost) always noun phrases, not clauses. Believe is thus intransitive here.
Incidentally, your example contains the further subordinate content clause that blue is my absolute favorite color, functioning as complement of the verb remembered.
EDIT: The case against the term 'noun clause' (and thus against clauses as objects), extracted from a paper by Huddleston & Pullum, authors of CGEL: