In a mixing bowl, combine the beaten eggs, heavy cream, and grated zucchini. Season with salt and pepper to taste. Set aside.

MAKE THE MEAT FILLING
In a skillet, heat 1 tablespoon olive oil over medium heat. Sauté the onion, garlic, and red bell pepper until softened.
Add the ground beef and ground pork, along with the oregano, cumin, and paprika or chili powder. Cook until browned. Season with salt and pepper to taste. Set aside.

MUSHROOMS
In the same skillet used for the meat filling, heat a little olive oil. Sauté the mushrooms until tender. Set aside.

ASSEMBLE THE ZUCCHINI CASSEROLE

In a medium baking dish, spread 1/3 of the zucchini mixture. Sprinkle with some of the sliced or shredded cheese and Parmesan.
Add the meat filling on top and sprinkle with more cheese and Parmesan.
Add another 1/3 of the zucchini mixture over the meat, then sprinkle with more cheese and Parmesan.

Spread the mushrooms over the top, then cover with the remaining zucchini mixture, cheese, and Parmesan.
Preheat the oven to 400°F (204°C) and bake for about 45 minutes.
The casserole should be set and golden on top.
Let it rest for 5 minutes before slicing and serving.