It's Cafe Eccell, and it is an old City building. The bakery (it is presumed) was once the city jail.
I worked there in college (6 years ago) as headwaiter for about 2 years. Donnie Anz was the owner at the time and he has since transferred ownership to Costa Dallis. Costa is a terrific guy, sort of short and squatty with almost no hair. He started at the restaurant as a pizza cook in the wood fired pizza oven. He brought a lot of the Greek flair to the restaurant.
I don't know who the current Head Chef is, but if its Peter (last name escapes), then you are in good hands. Peter is a true professional and doesn't overdo things the way some Chefs do trying to make a name for themselves.
The greatest thing about Eccell is the "in house" concept. Everything they prepare, down to the home grown herbs and even the spreads on the sandwiches are done in house. They have strong relationships with local vendors, even though the national and large sellers are way way way cheaper.
The desserts are terrific, usually changing. When I was there the favorite was the strawberry tart. My favorite was the Chocolate Amaretto Mousse Bombe & there was usually a great cheescake or two. If you enjoy the apertif, there was a great Rasperry flourless cake that went great with the local Messina Hof Port wine, one of the best ports anywhere.
As for non sugar filled foods, the pizzas are quite good and big enough to split for lunch...might try a salad. They probably don't mention it on the menu, but you can order a half salad and the greek is quite good.
The sandwiches are made from bread baked in the onsite bakery and filled with terrific stuff. They used to serve one on the foccia bread that included fresh mozzerella shipped in from Dallas Mozzerella Co., a small hole in the wall joint near Deep Ellum that has won tons of awards for their cheese.
Good wine list, otherwise well done menu. President Bush, Lyle Lovett & Julia Roberts, Gene Stallings, good ol' Tony Barone, RC & Wally, were all known to stop in and eat a bite. I had a chance to serve most of them. Lyle used to love the key lime pie and George would come with a group for various library related tasks when he was there.
As you can tell, I really enjoyed my time there and learned a lot about running your own biz. The folks at Eccell have a revenue generating machine and they know it. They've tried some other ventures (the original owner was actually a co-owner of the Chicken at one time with Ganter) but none have had the success of the little restaurant on Church St.