Separate egg white and yolks. Yolks into a metal bowl and whites into the mixing bowl.
Whisk the egg yolks with a pinch of salt and pepper until yolk has darkened a little. Add crème fraiche
Beat the egg white until it is light and fluffy.
Incorporate the egg white in 2-3 additions to the egg yolk mixture.
Heat up a fry pan over medium heat. Drizzle olive oil and the egg mixture into the pan. Smoothen the egg mixture in the fry pan with a rubber spatula and let it cook for 4-5 minutes, occasionally scrapping the sides to make sure it is not sticking. After the bottom has slight browning, slip the butter under the omelette. Cook for another 2 minutes.