Preheat oven to 350 degrees. Spray a baking sheet with cooking spray; set aside.
Place the olive oil in a skillet over medium heat; add the bell pepper-onion mix. Cook for 3 to 4 minutes, or until the vegetables are just tender. Remove from the heat. Stir in the parsley, chicken, 1 cup of pasta sauce, mozzarella, and ¼ cup of Parmesan cheese; stir.
Knead together 3 dinner roll dough balls and press into a 8- to 9-inch circle. Place the dough on a baking sheet. Place one fourth of the filling onto the center of the dough. fold the dough in half over the filling, crimping with a fork to seal. Continue assembling with the remaining ingredients.
Place the calzones in the preheated oven; bake for 20 to 30 minutes or until golden. Serve with the remaining sauce warmed and poured on top. Garnish with the remaining cheese.