Add the apples, walnuts, cinnamon, nutmeg and saute for 3 or 4 minutes.
Remove from skillet and keep warm.
Melt remaining butter while whisking the eggs with water.
Pour into skillet.
Tilt and rotate pan as the egg cooks.
Add the apple-walnut mixture to one side of the omlette, top with cheese and fold uncovered portion of omlette over top of the apple-walnut and cheese mixture.
Reduce heat to low and let set for 1-2 minutes.
Using a plastic spatula cut omlette in half and serve.