Place a large nonstick skillet over MEDIUM heat. Add the beef (or turkey), onion, bell pepper, and garlic and cook, stirring to break up the ground meat as it cooks. Continue to cook and stir until meat is thoroughly cooked and the veggies have softened. Drain off as much grease as possible and return the skillet to the heat.
Add the mushrooms, olives, marinara, pepperoni, Italian seasoning, black pepper, and crushed red pepper. Stir well to combine. Bring the mixture to a simmer, then reduce the heat to LOW, cover the pan, and allow to simmer for 15 minutes.
Meanwhile, preheat your oven's broiler. Split open the onion rolls and place them, inside facing up, on a baking sheet. Place the baking sheet in the oven for about 2 minutes, watching closely, until the rolls are toasted and lightly browned.
Remove the top buns from the baking sheet. Divide the filling between the bottom buns, sprinkle with mozzarella cheese, and return to the oven for a minute or two, just until the cheese is melted.
Remove from the oven and place the top buns on the sandwiches and serve.