Remove the skillet from the heat and let cool slightly. Stir in the cheese, salt, pepper, and cayenne sauce. Divide the mixture evenly into the mini tart shells. Crack 1 egg onto the top of each tart. Place the filled tart shells on a baking sheet.
Bake for 5 minutes for eggs with soft yolks. (If you like the egg yolks more solid, then leave in the oven and check every 1-2 minutes until the eggs have been cooked to the desired level of doneness.) Serve immediately.