Preheat the oven to 400°F (204°C) and grease a 9-by-13-inch baking dish. Brown the beef with half the salt and black pepper for 6–8 minutes.
Add the onion, bell pepper, and zucchini. Cook uncovered for 6–8 minutes. Stir in garlic, tomato paste, seasonings, and remaining salt; cook for 1 minute.
Add marinara and spinach and cook for 2–3 minutes. Reduce the heat and stir in cream cheese until smooth.
Transfer to the baking dish, top with cheddar and mozzarella, and bake for 12–15 minutes. Rest for 5–10 minutes before serving.