Preheat the oven to 450°F. Line a baking sheet with parchment paper or a Silpat.
Separate the eggs, adding the egg whites to one bowl and keeping the yolks inside the shells for easy transferring.
Add a pinch of salt and pepper to the egg whites then using a whisk (or a handheld beater or a stand mixer fitted with the whisk attachment), beat the egg whites until stiff peaks form. (See Kelly's Notes.)
Spoon the egg whites into two mounds on the baking sheet then make a deep well inside each mound. Bake the egg whites for 2 minutes.
Remove the baking sheet from the oven and place an egg yolk inside each well. Return the baking sheet to the oven and bake the eggs an additional 3 to 4 minutes or until the yolks have reached your desired doneness.
Remove the eggs from the oven, top them with the fresh chives and serve them immediately atop your choice of buttered toast.