Preheat oven to 425°F. Heat 1 tablespoon oil in heavy large skillet over medium-high heat. Add mushrooms and fennel seeds; sauté until mushrooms are brown, stirring often, about 5 minutes. Add garlic and oregano; stir 1 minute. Add spinach; stir just until wilted, about 1 minute. Transfer to medium bowl. Season with salt and pepper.
Line rimless baking sheet with parchment. Sprinkle paper with flour. Roll out dough on lined baking sheet to 15x10-inch rectangle. Sprinkle 3 tablespoons Parmesan crosswise over half of crust, leaving 1-inch plain border. Top with 3/4 cup Fontina, then mushroom mixture, distributing evenly. Sprinkle 2 tablespoons Parmesan and 3/4 cup Fontina over mushrooms. Spoon dollops of ricotta cheese over; sprinkle with crushed red pepper. Fold plain half of dough up over filling. Crimp edges tightly to seal. Brush with oil.
Bake calzone until puffed and brown, about 18 minutes. Brush with oil and serve.