Rub the inside of a 6 ounce ramekin with butter. Pour cream into the ramekin, then crack the eggs on top of the cream without breaking the yolks. Use a spoon to position the yolks towards the center of the ramekin, then sprinkle with salt, pepper, chives, and Parmesan cheese.
Bake in preheated oven until the whites of the eggs have set and the yolks are still soft, 12 to 15 minutes. Remove from oven, and allow to set for 2 to 3 minutes before serving.