Azuca on South Alamo offers a really tasty Cuban. I don't know about the authentic bread, but the sandwich as well as other offerings from Chef Rene Hernandez are delicious. When you are tired of Cuban sandwiches, try the seafood soup/stew. A real taste treat.
Also the desserts are lovely, as well as being delicious. I've taken my group to this restaurant several times.and everyono always enjoys the food.