In covered saucepan over medium-low heat, cook leeks and stock until leeks are softened, 12 to 15 minutes.
Uncover and cook over high heat, stirring almost constantly, until moisture has evaporated.
Add cream, butter, and salt and pepper to taste.
Keep warm or reheat before filling omelets.
To fill omelet, spread about 1/4 of mixture in row across centre of omelet at right angles to handle of pan and roll the omelet.