Actually the first part just says the topic of the sentence is
an omiai partner. I don't think there's any connection with
The second part you don't really need to already know the idiom to understand it.
Let's focus on 理想を絵に描いたような. The parts before the ~ような is actually a clause by itself. ような means like or similar to.
For that clause, the を particle tells is that 理想 is the direct object. What's the verb for it? 描いた. So we know the clause's main action is 理想を描いた:
Next, we need to figure out what 絵に means. The に here describes the target of the clause: the depiction as/into a painting. 理想を絵に描いた thus means
An ideal depicted as a painting.
Then, 理想を絵に描いたような男性だった means
A man who was like an ideal depicted as a painting
Using more idiomatic English, you might get something similar to the explanation you were given. And if you connect it with the first part, you'll see that the man that is being described is the omiai partner.