Eggs, Hash Browns, & Ham Casserole

12 large eggs
1 cup cream
1 teaspoon salt
1/2 teaspoon pepper
3/4 cup olive oil
1/2 teaspoon butter flavoring
2 cups hash brown potatoes, shredded, frozen, thawed
1 pound sliced ham, chopped
1/4 cup onion, chopped
1 cup sharp cheddar cheese, grated