I noticed that nobody has answered your question. I am not sure how much I can help. My whole family was in Sofia and Varna a couple of years ago. I don't remember any specific restaurants but the food is great. Mostly combination Mediterranean/Turkish with some Eastern European influence.
We went to a restaurant with a bulgarian musical group. we had seen the ad in one of the tourist free journals in the hotel and it turned out to be great.
Do not go to any fancy place or any restaurant in hotels.
We had a great time.