Preheat your oven to 350°F (175°C) and grease a baking dish with butter or oil
Crack all eggs into a large mixing bowl
Add heavy cream, salt, pepper, garlic powder, and paprika
Whisk thoroughly until the mixture becomes smooth and slightly frothy
Add diced ham into the egg mixture and stir gently
Fold in half of the shredded cheddar and mozzarella cheese
Pour the mixture evenly into the prepared baking dish
Distribute cream cheese cubes evenly throughout the mixture
Sprinkle remaining shredded cheese over the top
Lightly tap the dish on the counter to remove air bubbles
Place the dish in the oven on the center rack
Bake for 30–40 minutes until the center is set and edges are golden
Insert a knife in the center; it should come out clean when done
Optional: broil for 2–3 minutes for a golden cheesy top
Remove from oven and let rest for 5–10 minutes
Garnish with chopped parsley
Slice into squares and serve warm