Preheat the oven to 350 degrees.
Pour the can of crushed tomatoes into a small bowl. Finely mince the garlic and toss in with the tomatoes (I like to use my microplane to do this since the garlic won’t burn in the sauce and this way you won’t get large chunks of raw garlic while you eat). Stir in the oregano, salt, sugar and pepper. Set aside.
Prepare the rolls: Cut off just the very top crust of the roll. Use your fingers to pull out the bread from inside the roll, creating a bowl. Be careful not to pull too much off from close to the sides and bottom as you don’t want the ingredients to leak out. You will want the sides and bottom to be about ½-3/4” thick. (Toast up the bread you pulled out to use as croutons in a soup or salad to avoid waste!).
Heat the cooking oil in a sauté pan over medium-high heat. Add the onion and sauté for about 2-3 minutes or until tender. Add the ground beef to the pan and season with salt and pepper. Break up the meat as it cooks with a wooden spoon, stirring frequently until the meat is no longer pink. Remove from the heat and drain using a metal colander. Set aside.
Place the “bread bowls” onto a baking sheet. Spread the bottom of each with a good portion of the sauce. Then divide the ground beef mixture among the rolls (you don’t want these to over flow too much, so use less beef if necessary). Layer the mushrooms and the pepperoni on top of the beef. Now top the each bun with the mozzarella cheese. The mixture/cheese should come just barely above the top of the bun as it will sink a little as it cooks.
Cook the deep dish pizzas for about 15-20 minutes, until the cheese is melted and bubbling, the bread is slightly toasted, and the ingredients are warmed through. Let sit for about 5 minutes before serving.