Heat oven to 400°F. Lightly spray cookie sheet with cooking spray. In 10-inch skillet, cook sausage over medium-high heat 6 minutes, stirring frequently, until no longer pink. Remove sausage to bowl. In same skillet, heat oil over medium-high heat. Cook bell pepper and mushrooms in oil 5 minutes, stirring frequently, until tender. Add vegetables to sausage. Stir in olives, oregano, basil and red pepper flakes.
Unroll dough on cookie sheet. Starting at center, press dough to 14x10-inch rectangle; cut into 4 (7x5-inch) rectangles. Spoon 1 slightly heaping tablespoon pizza sauce onto each rectangle to within 1/2 inch of edge. Top half of each rectangle with sausage mixture and cheese, spreading to within 1/2 inch of edge. Fold dough in half over filling; press edges firmly with fork to seal. Brush with egg.
Bake 20 to 25 minutes or until golden brown. Serve warm calzones with warm pizza sauce for dipping.