Heat 2 teaspoons of the oil in a large skillet over medium heat.
Whisk together the eggs, milk, salt, and black pepper. Pour half of mixture into hot skillet. When egg starts to cook, lift edges with a spatula to allow uncooked egg to slide underneath. When almost cooked through, top 1 half with desired toppings. Fold over untopped side and cook 2 minutes, until egg is cooked through and cheese melts (if using cheese). Transfer omelet to a baking sheet and place in a warm oven while you prepare second omelet.