Hi Shane - Have never been to California, so no help on commenting on the restaurant you mentined. If you want to make a deep dish, there are several excellent recipes on this forum. I have found using a Kitchenaid with a dough hook set on mix for two minutes max, and no kneading, let the dough rise for a good hour or so, punch it down, and place it in the fridge for a day for a cold ferment really aids in the flavor of the crust.
For sauce, I drain a 28 oz. can of whole crushed tomatoes (6in1 is my favorite brand, but there are others that are good as well). Then add a few (3 or 4) cloves of crushed garlic, 1-1/2 t each of whole fennel, oregano, and basil, then a touch of salt. Amounts can be varied to suit individual taste. - Mazz