Preheat the oven to 350°F (175°C).

In a skillet over medium heat, cook the ground beef until browned. Drain excess fat.

Add chopped onion, bell pepper, and mushrooms to the skillet and sauté until softened.

In a mixing bowl, whisk together the eggs, heavy cream, garlic powder, onion powder, salt, and pepper.

Combine the beef mixture with the egg mixture and stir in the sugar-free ketchup.

Pour the mixture into a greased casserole dish and top with shredded cheddar cheese.

Bake in the preheated oven for 25-30 minutes, or until the cheese is bubbly and golden.