In a small bowl, whisk the eggs with salt and pepper until the yolks and whites are fully combined.
Place a non-stick skillet over medium-low heat and melt the butter, swirling to coat the surface.
Pour the egg mixture into the skillet and cook undisturbed for 1-2 minutes until the edges begin to set.
Using a spatula, gently lift the edges and tilt the pan to allow uncooked egg to flow underneath.
Once the top is mostly set but still slightly moist, spoon the cottage cheese onto one half of the omelette.
Sprinkle with fresh chives, then fold the other half over the filling.
Cook for an additional 30-60 seconds to warm the cheese through.
Slide the omelette onto a plate and serve immediately.