Prepare all of the ingredients. Place pizza stone on grill and preheat to medium-high
In a bowl, add all sauce ingredients. Use your hands to break up the whole tomatoes and mix the sauce, leaving some chunks.
On a lightly floured cutting board (big enough for 4 pizzas), place the four pieces of dough. Gently fold over the edges of each piece to make a small crust.
Add roughly 2 tbsp of sauce to each pizza, spreading to edges. Sprinkle with about a tablespoon of parmesan. Top with ham, pepperoni, and mushrooms. Sprinkle with another tablespoon of cheese and some Italian seasoning.
Once grill is hot, transfer pizzas from cutting board to pizza stone (carefully!) and close lid. Cook for 15-20 minutes. Remove and let cool for 2-3 minutes before cutting into quarters
Repeat with second round of pizza. (NOTE - my stone can only handle 4 pizzas at a time. If you can get more in there, go for it!)
***NOTE*** You can use different toppings for these pizzas - just like any homemade pizza.