Place a pizza stone in the oven and preheat the oven to 500°F. Do this 30 minutes prior to cooking the pizza.
Make the pizza dough and pizza sauce. You can also use store bought pizza dough or pizza sauce. Divide 1 1lb of dough into 2 even pieces. Let rest on a lightly floured surface while you prepare the toppings. In a medium skillet, heat the olive oil to medium high heat. Add the mushrooms and cook for about 5 minutes, stirring occasionally, until the mushrooms are tender and golden brown. About one minute before the mushrooms are done, stir in the garlic. Season with salt and pepper.
Make sure all of your other toppings are ready to go before you start making the pizza.
Sprinkle a pizza peel lightly with flour and set aside. If you don’t have a pizza peel, you can use the back of a rimmed baking sheet or a rimless baking sheet.
On a lightly floured surface, start with one dough ball and use your fingers to gently press the dough into a circle. Gently stretch the dough into a 10 to 12-inch circle, being careful to not over stretch the dough.
Spread the pizza with half of the pizza sauce, leaving a 1-inch border without sauce. Sprinkle the pizza evenly with half of the shredded mozzarella cheese. Top with half of the toppings: cooked mushrooms, artichoke hearts, roasted peppers, red onion, and olives.
Once you have the toppings on the pizza dough, you need to move quickly so the pizza is easy to transfer to the oven.
Use the pizza peel to carefully transfer the pizza onto the hot pizza stone. Bake until the cheese is melted, and the crust is golden brown, about 8 to 15 minutes.
When the first pizza is almost done baking, make the second pizza, following the same steps. When you remove the first pizza from the oven, transfer the second pizza to the oven and bake.
Garnish the pizzas with fresh basil, crushed red pepper flakes, and Parmesan cheese, if desired. Slice and serve immediately.