Preheat oven to 200°C / 390°F (180°C fan) and separate the egg whites into a bowl.
Heat olive oil in an 8-inch ovenproof skillet over medium heat, cook asparagus until tender, then add beef bacon and stir briefly, transfer to a bowl.
Melt butter in the same skillet over low heat until bubbling gently but not smoking.
Whisk egg whites until fluffy, just opaque, and creamy, then stir in chives, salt, and pepper.
Pour egg whites into skillet, spread evenly, stir gently for about 10 seconds until the base sets, then tap the pan a few times to release bubbles.
Sprinkle asparagus, beef bacon, and cheese over one half of the omelette, then transfer skillet to oven for 2 minutes.
Remove from oven, fold omelette in half over filling, press edge gently against the pan for 30 seconds to seal, then slide onto a plate and garnish with extra chives.