Heat skillet with a teaspoon vegetable oil. Cook green onion for a minute or so, until aroma is released.
In a mixing bowl, beat eggs by hand with dill and green onion for about a minute.
Pour one half of the mixture into a buttered hot skillet and cook over medium heat, lifting edges with spatula several times to allow uncooked egg to run to bottom of skillet.
When bottom of omelet is firm, turn gently with spatula. Crumble 2 oz of smoked salmon on cooked eggs, and top with 1 oz strips of cream cheese.
Fold the other half-circle over the top of the half with the ingredients, cover skillet with lid, and cook for a minute or two over low heat. Serve with buttered toast or toasted bagels.
Make the second omelet.