Preheat the oven to 475°F (245°C) with a pizza stone or heavy baking sheet inside for at least 30 minutes.
In a medium skillet over medium heat, cook the Italian sausage, breaking it up with a spoon, until browned and no longer pink; drain excess fat and set aside.
Thinly slice the green bell pepper, red onion, and mushrooms.
Lightly dust a pizza peel or large, flat baking sheet with cornmeal or semolina.
Gently stretch or roll the pizza dough into a 12–14-inch circle and transfer it to the prepared peel or baking sheet.
Brush the dough’s edges with olive oil to help form a golden crust.
Spread the pizza sauce evenly over the dough, leaving a 1-inch border for the crust.
Sprinkle half of the shredded mozzarella over the sauce; top with cooked Italian sausage, sliced pepperoni, green bell pepper, red onion, and mushrooms; finish with the remaining mozzarella, dried oregano, and red pepper flakes.
Carefully slide the assembled pizza onto the hot pizza stone or baking sheet and bake for 10–15 minutes, until the crust is golden brown and the cheese is bubbly and lightly browned.
Let the pizza cool for a few minutes before slicing and serving.