In a small skillet or omelet pan, heat half the oil until hot.
Add the onion and sauté until the onions begin to look soft.
Add the green pepper and continue cooking until the onion is transparent and the peppers are soft. Remove the onions and peppers to a small dish. You will add them back a little later.
In a medium bowl, whisk the eggs, milk, herbes de Provence, nutmeg, salt and pepper until frothy.
Heat the remaining oil in the skillet until it is hot. Then pour in the egg mixture and cook over medium or medium-low heat until set.
Don't let your pan get too hot, or you will brown the omelet more than you might like. Keep an eye on how the underside is coming along.
As you cook the eggs, lift the sides up with a spatula and tilt the skillet to allow the eggs that are as yet uncooked to flow around the cooked part. This helps to get all the eggs evenly cooked. Keep doing this until the eggs are almost firm.
Turn the almost set eggs over in the pan to finish cooking.
Sprinkle the onion and pepper mixture over one-half of the omelet. Add the smoked salmon evenly over the omelet and sprinkle on the cheese.
Fold the half of the omelet that is plain over the one with the goodies and continue to cook it until the cheese starts to melt and the salmon is hot, maybe 1 minute.
If you are making this entire recipe, it serves 2, so cut the omelet in half before you serve it.
Slide the omelet(s) off the pan onto a plate and garnish with tomatoes or some herbs.