Preheat the oven to 230°C/450°F/Gas 8. Line a large, rimmed baking sheet with parchment paper and set it aside.

Crack and separate the eggs, placing the whites in a large mixing bowl and reserving the yolks in another bowl. For best results, reserve the egg yolks in small, individual dishes rather than in one larger bowl.

Season the egg whites with salt and pepper, to taste.

Using a hand mixer or immersion blender, beat the egg whites until stiff peaks form. Scrape the sides of the bowl with a spatula while blending to incorporate all of the egg white.

Gently fold in two-thirds of the Asiago cheese and chives into the bowl, being careful not to deflate the egg whites in the process. Spoon the whipped egg white mixture onto the prepared baking sheet into four piles, leaving plenty of room between each mound. With the back of a spoon, create an indent in the center of each mound and place the baking sheet on the center rack in the preheated oven and bake for 3 minutes.

After 3 minutes, remove from the oven and transfer reserved yolks into the indent of each mount. Sprinkle each mound with half of the remaining cheese and fresh chives and return to the oven. Bake another 3 minutes or until yolks are set and egg whites are golden brown.

Remove the egg clouds from the oven and sprinkle with remaining cheese and chives and serve immediately.