Preheat the oven: Set to 375°F (190°C).
Grease a 9x13-inch baking dish with olive oil or butter.
Brown the beef: Heat a large skillet over medium-high. Add beef and cook, breaking it up, until browned and no pink remains. Drain excess fat if needed.
Sauté aromatics and veggies: Add onion and olive oil to the skillet.
Cook 3–4 minutes until softened. Stir in garlic, zucchini, mushrooms, and riced cauliflower. Cook 5–6 minutes until most moisture cooks off.
Season the mixture: Stir in smoked paprika, oregano, chili powder (if using), salt, pepper, and tomato paste.
Mix well and cook 1 minute to bloom the spices. Remove from heat.
Make the creamy binder: In a bowl, whisk eggs, heavy cream, and cream cheese until mostly smooth. Small specks are fine.
Season with a pinch of salt and pepper.
Combine and layer: Fold the egg mixture into the beef and veggies. Stir in half the cheddar and all the mozzarella. Spread evenly in the prepared baking dish.
Top with remaining cheddar.
Bake: Bake uncovered 22–28 minutes, until the center is set and the top is golden and bubbly.
Rest and serve: Let it rest 5–10 minutes to set. Garnish with chopped parsley or green onions. Slice and serve.