Preheat the oven to 450°F (230°C). Line a large baking sheet with parchment paper or foil and lightly coat it with olive oil spray; set aside.
Slice each chicken breast horizontally to create two thin cutlets (about 1/4 inch thick). Place a cutlet between pieces of wax or parchment paper and gently pound with a meat mallet or rolling pin until even.
Season both sides of each cutlet with 1/4 teaspoon kosher salt (total) and freshly ground black pepper to taste.
Arrange the fillings on the center of each cutlet: about 1 tablespoon shredded mozzarella, 3 slices turkey pepperoni, and 3 slices white button mushroom. Roll each cutlet up tightly and place seam-side down on the prepared baking sheet.
In a small bowl, mix the 1/4 cup breadcrumbs with 2 tablespoons grated Parmesan. In another small bowl, whisk together 1/2 tablespoon olive oil and 1 tablespoon lemon juice with a pinch of pepper.
Dip each chicken roll-up briefly into the oil-lemon mixture, then coat evenly with the breadcrumb-Parmesan mixture. Place seam-side down on the baking sheet and lightly spray or brush the tops with oil.
Bake the roll-ups at 450°F for about 20 minutes, until the chicken is almost cooked through.
Remove the baking sheet from the oven and evenly top each roll-up with marinara sauce, a sprinkle of the remaining mozzarella, red onion slices, and chopped green bell pepper.
Return to the oven and bake 4–5 minutes more, until the cheese is melted and the sauce is heated. Serve immediately.