Preheat your oven to 180°C (350°F). Lightly butter two small oven-safe ramekins, approximately 150–180 ml each.
Divide the cream evenly between the ramekins. If you are using mushrooms, spinach, or ham, add a small amount to each dish. Season lightly with salt and freshly ground black pepper.
Carefully crack one egg into each ramekin, keeping the yolk intact. Spoon any remaining cream around the egg rather than directly over the yolk. Sprinkle with grated cheese if desired.
Place the ramekins in a deep baking dish. Carefully pour hot water into the baking dish until it reaches approximately halfway up the sides of the ramekins. Take care not to splash water into the eggs.
Transfer the baking dish to the preheated oven. Bake for approximately 12–18 minutes, checking the eggs toward the end of cooking. The whites should be set, while the yolks can remain soft if that is your preference. Cooking time depends on ramekin size, oven accuracy, and the desired doneness.
Carefully remove the ramekins from the water bath using oven mitts. Allow them to rest briefly, then sprinkle with fresh chives and black pepper. Serve hot with toasted baguette slices for dipping into the creamy eggs.