Peel shallot and finely chop. Separate eggs. Beat egg whites with 1 pinch of salt until stiff. Mix yolks with 2 tablespoons creme fraiche, mustard, lemon juice and finely chopped basil. Season with salt and pepper and loosely fold in egg whites.
Add half of butter to a nonstick frying pan. Add half of shallot and saute. Pour in half of egg mixture and cook for 6-8 minutes or until bottom is golden brown. Remove pan from heat when done.
Spread 1 tablespoon creme fraiche on the omelet and top with half of crumbled feta. Season with salt and pepper and fold omelet using a pan.
Repeat to make second omelet.
Serve omelets garnished with basil.