Preheat your oven to 425°F and lightly grease a 12-cup muffin pan with butter or cooking spray, making sure each cup is evenly coated to prevent sticking. While the oven heats, grate your Parmesan cheese finely (you'll want about 10 oz total) and mince the fresh chives. Measure out your heavy cream and have salt and pepper nearby. This prep work takes just a few minutes and ensures everything is ready when you need it.

Crack one egg into each cup of the prepared muffin pan, keeping the yolks as intact as possible. To each egg, add about 1 teaspoon of the heavy cream, a small pinch of salt, a crack of fresh pepper, and roughly 1 tablespoon of the grated Parmesan cheese. I like to reserve about 2 tablespoons of cheese for topping after baking—it creates a golden, crispy top that looks restaurant-quality. Don't overfill the cups; leave a little room at the top so the eggs can puff slightly as they bake.

Place the muffin pan into the preheated 425°F oven and bake for 7-12 minutes depending on your preferred doneness: 7-8 minutes for soft, runny yolks with set whites; 9-10 minutes for medium yolks that are slightly jammy; or 11-12 minutes for fully set, firm yolks. Start checking at the 7-minute mark by gently jiggling the pan—the whites should be set but the centers should still have some movement if you prefer them soft. The eggs will continue to cook slightly after removal from the oven.

Remove the muffin pan from the oven and immediately sprinkle the reserved Parmesan cheese over the top of each baked egg, allowing it to melt slightly from the residual heat. Top each egg with a small pinch of the minced fresh chives for color and a fresh onion flavor. Carefully run a small knife around each egg cup to loosen them, then either serve directly in the pan for an elegant presentation or gently transfer to individual plates. Serve immediately while the eggs are still warm and the cheese is melted.