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.
My trick for making sure the egg yolks don’t break is cracking them into a glass or cup first, then gently sliding them into the casserole dish.
You can also use Comte cheese instead of Gruyere.
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