Preheat the oven to 450°F. Coat two baking sheets with nonstick cooking spray. In a 10-inch skillet heat olive oil over medium; add the mushrooms and cook until liquid has evaporated, about 6 minutes. Add the ground beef to skillet. Cook until browned; drain off any fat. Stir in 1/2 tsp. of the salt and 1/4 tsp. of the black pepper.

In a medium bowl combine the ricotta cheese, spinach, garlic, crushed red pepper, and remaining 1/4 tsp. each salt and black pepper.

Divide the dough into six portions; shape each into a ball. For each calzone, on a lightly floured surface roll one dough ball into a 7-inch circle. Spread about 1/3 cup ricotta mixture on one half of the dough circle, leaving a 1-inch border. Top ricotta with about 1/2 cup of the meat mixture and 2 Tbsp. mozzarella. Lightly brush the edges with water. Fold the dough over filling; seal with the tines of a fork. Transfer the calzones to a prepared baking sheet. Repeat with remaining the dough and fillings.

Brush the calzones with milk (if using). Prick the tops with a fork or paring knife. Bake, rotating sheets once, until golden and hollow when tapped, 15 to 20 minutes. Cool slightly. Serve with warmed marinara sauce.