Preheat oven to 450°F. Bring 1 inch of water to a boil in a small pot. Place broccoli in a steamer basket, place steamer basket in pot, cover and steam until tender, 4 to 5 minutes. Let cool slightly, coarsely chop, and place in a medium-size bowl. Stir in garlic, ricotta, mozzarella and egg yolk; season with salt and pepper.
Divide pizza dough into 4 portions and use a rolling pin to roll each into an 8-inch circle. Place a quarter of broccoli mixture in center of a round, fold dough in half, and then seal by rolling edges together toward center and crimping. Using a sharp knife, cut two small slits in top of calzone to let steam escape. Repeat with remaining dough and broccoli mixture. Brush calzones with olive oil.
Mist a large, rimmed baking sheet with nonstick cooking spray. Place calzones on baking sheet and bake in center of oven until golden and risen, 13 to 15 minutes. Serve immediately, with warm tomato sauce on the side for dipping, if desired.