"it's a delicious dessert, doubly so when you use cream instead of milk"
I know the word "doubly" means "in two ways" here. But why there is a add-on "so"?
Essentially, doubly so means even more so. It does not refer to a literal doubling of any quantity. Since it usually refers to intangible concepts, this ambiguity is unimportant.
It doesn't mean in 'two ways'. I means that it is 'twice' of whatever it is describing. The dessert is delicious. But when you add cream instead of milk, it becomes two times tastier. As simple as that. In simple terms, you eat the dessert by adding milk and you're like "Yumm". But when you add cream instead of the milk, you'll be like "Yummmmmmmmmmmmmmmmmmmmm". (Not that the number of 'm's are doubling, but you get the idea).
The example sentence does not seem to be a very good sentence. So and thus are usually adverbs that can mean (in) this way or (in) this manner. Consider:
Jane so closed the door.
In both exampes, so in an adverb.
Jane loudly closed the door.
Only in this sense, does so "stand for" loudly. It is used as a substitute adverb, so to speak. And it means (in) this manner (and the manner is loudly).
Now, when you read the example sentence, it is hard to see so functioning as an adverb. And therefore I believe it is a bad or poor sentence.
If the sentence were:
The cake is delicious when you use milk (to make it), doubly so when you use cream instead of milk.
Here there seems to be a process or activity implied (the making of the cake), which the initial example sentence does not have. When there is a process, you can use an adverb such as so or thus.
Doubly can mean in two ways but it usually just means twice as much.