Beat eggs in a bowl with an electric mixer until thick and frothy, 1 to 2 minutes. Fold in parsley, black pepper, salt, and white pepper.
Melt butter and olive oil together in a nonstick skillet over medium heat; reduce heat to low. Cook and stir egg mixture in hot butter and oil until eggs begin to set, about 1 minute. Stir in 1 tablespoon creme fraiche; cook and stir until eggs are set, 2 to 3 minutes more. Transfer to a plate and garnish with remaining creme fraiche.