In a large bowl, whisk together eggs and milk. Add shredded cheddar cheese, diced ham, diced onion, diced bell pepper, onion powder, garlic powder, Italian seasoning, salt, and black pepper. Mix well.

Pour the egg mixture into a greased 9-inch square baking dish.

Bake in the preheated oven for 40-50 minutes, or until the eggs are set and the top is slightly golden. Check doneness by inserting a knife in the center; it should come out clean.

Let the omelette cool for a few minutes before slicing. Serve warm.