Preheat the oven. Set your oven to 450°F (230°C). Line a baking sheet with parchment paper suitable for this temperature.
Separate the eggs. Carefully separate the egg whites from the yolks. Place all four whites in a large, clean mixing bowl and keep each yolk in its own small bowl, making sure the yolks remain intact.
Whip the egg whites. Using an electric mixer, beat the egg whites until they form stiff peaks. The whites should be thick, glossy, and able to hold their shape.
Fold in the ingredients. Gently fold the grated Parmesan cheese, chopped chives, and cooked crumbled bacon into the whipped egg whites. Avoid overmixing so the mixture stays light and airy.
Shape the clouds. Divide the egg white mixture into four fluffy mounds on the prepared baking sheet. Use the back of a spoon to create a deep well in the center of each mound.
Bake the egg whites. Place the baking sheet in the preheated oven and bake for 3 minutes, allowing the whites to begin setting and turning lightly golden.
Add the egg yolks. Carefully remove the baking sheet from the oven. Gently slide one egg yolk into the center of each cloud. Season with black pepper.
Finish baking. Return the baking sheet to the oven and bake for another 2–3 minutes, or until the whites are set and the yolks reach your preferred doneness. For fully cooked eggs, continue baking until both whites and yolks are firm.
Serve immediately. Carefully lift the cloud eggs from the parchment using a thin spatula and serve while warm and fluffy.