Preheat the oven to 190 degrees C. Boil water in a kettle.
Grease a mini lidded casserole dish with olive oil. Distribute the diced ham over the bottom, then sprinkle with 1 tablespoon grated cheese. Pour the cream on top and add a small amount of pepper.
Crack the eggs into the casserole dish one at a time. Make sure the egg yolks remain intact. Here is a little trick. Crack the egg into a glass or a cup first, then gently slide them in. Sprinkle with the remaining cheese and some chopped fresh chives. Season with salt and pepper to taste.
Cover the casserole dish and place it in a roasting tin. 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, then remove the lid and cook for an additional 3 to 6 minutes, until the egg whites are just set but the yolks are still runny. Depending on the oven the total cooking time is 12 to 15 minutes. Serve hot with toast or strips of bread to dip in the egg yolks.