1. Place a rack in the lowest position in oven and preheat to 450°F. Line 2 large baking sheets with parchment.
2. In a large skillet, warm oil over medium-high heat. Add mushrooms; sauté until softened, about 3 minutes. Add meat mix and cook, breaking up with a wooden spoon, until browned, about 5 minutes. Add spinach and 1 cup marinara sauce and cook, stirring, until spinach has wilted, about 2 minutes. Remove from heat.
3. On a lightly floured work surface, divide dough in half. Roll one portion into a large oval, about 13 inches wide by 16 inches long. Spoon half of meat filling onto center of dough, leaving a 2 1/2-inch margin around the edges. Top with 1 cup mozzarella. Fold dough in half along the width and seal; transfer to lined baking sheet. Using a sharp knife, make 3 slits on top of dough. Repeat with remaining dough, filling and cheese.
4. Bake until crust is golden and filling is bubbling, about 18 minutes. Warm remaining marinara sauce in microwave or in a saucepan over medium-low heat. Remove calzones from oven, slice each into 4 pieces and serve, passing warmed marinara on the side.