1. Preheat oven to 475F.
2. Cut bread into cubes and toss together with melted butter. Bake for 2-3 minutes, until golden. Remove from the oven and set aside.
3. Turn heat down to 350F.
4. Sauté onion in olive oil until softened.
5. Whisk eggs, half and half, salt, pepper, thyme leaves and nutmeg in large mixing bowl.
6. Place toasted bread in a buttered baking dish and toss together with onions, ham and 3 cups white cheddar.
7. Pour egg mixture over bread and press down on the bread to ensure all cubes are soaking up the custard. Top with remaining cup of cheese.
8. Bake for 45-50 minutes, or until a fork inserted in the middle comes out clean. I recommend letting it rest for 5-10 minutes before serving.
9. Store any leftovers in the refrigerator for up to 2 days.
If substituting fresh thyme leaves for dried, use half the amount.