Deep-dish pizza is controversial. You either love it or you hate it, because it makes a big statement. Taking forty-five minutes to prepare, a deep-dish pizza has a crust built more like that of a cheesecake (but not sweet) than that of a classic Neapolitan pizza. The crust fades into the background, overwhelmed by the inch-and-a-half mass of tomato sauce, cheese, meats and vegetables. It's almost a casserole. This kind of pizza has only rarely been available around New Orleans. That's Amore has a monopoly on the style at this writing.
That's Amore originally opened under a different name in 2006. It has since been sold at least once, but the food has remained stable and reliably good.
The dining room is Basic Pizzeria: pleasant enough to eat in, but clearly a neighborhood cafe. Lots of the customers get take-out.
Give the deep-dish pizzas plenty of time for preparation. You can't come in here right before they close and get one of those. Get it once if you never had one, but know that eating a deep-dish pizza can be messy, and that the thin crust job is better. The large pizzas are a much better deal than the small ones. Apparently no math majors work here, so the biggest thin-crust pizza costs three times as much as a small one, but is five times as large.