"Oeufs cocotte is a French way of baking eggs in a water bath in the oven - you can add other ingredients as well but ham and cheese is one of the easiest variations. Oeufs cocotte taste best served hot with toast or strips of bread to dip in the egg yolks. [Recipe originally submitted to Allrecipes.fr]"
Preheat the oven to 375 degrees F (190 degrees C). Boil water in a kettle.
Grease a small lidded casserole dish with olive oil. Distribute diced ham over the bottom and sprinkle with 1 tablespoon Gruyere cheese. Pour cream on top and season with a little pepper.
Crack eggs into the casserole dish one at a time, making sure egg yolks remain intact. Sprinkle with remaining 1 tablespoon Gruyere cheese and fresh chives. Season with salt and pepper. Cover casserole dish and place into a roasting pan. Pour in enough boiling water so it reaches about halfway up the casserole dish.
Bake in the preheated oven for 9 minutes with the lid on. Uncover and continue baking until the egg whites are just set but the yolks are still runny, 3 to 6 additional minutes.