Preheat oven to 375°. In a medium bowl, whisk eggs, mozzarella, and cream; season with salt, black pepper, and red pepper. In a large ovenproof skillet over medium heat, heat oil. Add shallot and garlic and cook, stirring occasionally, until shallot is translucent, about 5 minutes. Add mushrooms and cook, stirring occasionally, until softened, about 5 minutes more. Add spinach and cook, stirring frequently, until wilted, about 2 minutes; season with salt and black pepper. Pour egg mixture into pan over vegetables. Dollop with ricotta. Bake frittata until eggs are just set and edges are golden brown, about 12 minutes.