Clean the asparagus and bend each stalk to snap off the woody end. Add the asparagus to a pot of boiling salted water over medium heat. Cook for about a minute, then remove from the pot and place under cold running water to stop the cooking process. Drain and set aside. Chop 2 asparagus on smaller chunks.
In a bowl season beaten eggs with salt and pepper. Heat a non-stick frying pan or skillet over medium-high heat. Add the olive oil and butter. When the butter is foaming and is completely melted, pour the eggs quickly into the pan. Shake the pan to distribute the eggs evenly, then leave for about 20 seconds for the eggs to set.
Cook the omelette
Spread chopped asparagus and grated cheese on top of the eggs. Cook the omelet until the eggs are softly set. Gently run a rubber spatula around the edge of the omelet for the uncooked eggs to flow underneath so it cooks nicely. It will take about a minute.
Slide the omelet onto a plate, folding it in half. Add the rest of the blanched asparagus in the middle. Serve immediately with freshly chopped chives. Optionally you can serve with watercress, grated cheese, a drizzle of olive oil and a dollop of sour cream. Enjoy.