Caramelized Apple Omelet

Directions

1. 1
   Melt butter in a 12-inch nonstick skillet over moderate heat until foam subsides.
2. 2
   Add sugar and cook, stirring, until dissolved, about 1 minute.
3. 3
   Add apple and cook, turning slices over once, until golden and just tender, 5 to 8 minutes.
4. 4
   Whisk together eggs with a pinch of salt.
5. 5
   Pour eggs over apple and cook over moderately low heat, lifting up cooked egg around edge occasionally with a heatproof rubber spatula to let raw egg flow underneath, until omelet is set but top is still slightly moist, about 2 minutes.
6. 6
   Dollop creme fraiche and dulce de leche across center of omelet.
7. 7
   Fold bottom third of omelet over filling using a heatproof plastic spatula.
8. 8
   Holding skillet over a plate, carefully tilt skillet until omelet slides out and almost half is touching plate, then turn skillet upside down, as if trying to cover plate, to make omelet fold over itself.
9. 9
   Cut omelet in half and divide between 2 plates.
10. 10
    *Available at Latino markets, specialty foods shops, and some supermarkets.