Preheat your oven to 375°F (190°C). Generously grease a 9-inch pie plate or quiche dish with butter.
In a large mixing bowl, whisk together the 6 large eggs and 1 cup of heavy cream until the mixture is smooth and well-combined.
Stir in the diced ham, 1 cup of the shredded cheddar cheese (reserving the other 1/2 cup for the topping), chopped chives, salt, and black pepper. Mix until all ingredients are evenly distributed.
Pour the egg mixture carefully into the prepared pie plate.
Sprinkle the remaining 1/2 cup of shredded cheddar cheese evenly over the top of the quiche.
Bake for 30-35 minutes, or until the center is just set (it should not jiggle) and the top is golden brown. A knife inserted near the center should come out clean.
Let the quiche cool for at least 10 minutes before slicing and serving. This allows it to set up properly.
Notes
Storage: Store leftover quiche in an airtight container in the refrigerator for up to 4 days. Reheating: Reheat individual slices in the microwave or in an oven at 350°F until warmed through. Variations: Feel free to add 1 cup of cooked, well-drained spinach or sauteed mushrooms. You can also swap the cheddar for Gruyère or Swiss cheese for a different flavor profile.