Heat up your pan on the stove top. Add the butter and wait for it to melt.
Pour the egg into the pan. I like to give it a quick whisk when I put it in the pan then leave it to cook in one piece. sprinkle cheese, broccoli , salt and pepper on top of the egg. I cover the pan because I like the egg to be well cooked, but this will depend on your taste. Once the cheese starts to melt and you can see that the omelette is cooked through on the edges, then you can fold it over.
Start by shaking the pan and gently tilting the pan so that the omelette slides to the edge. Place your spatula under the part of the omelette that has slid to the edge of the pan and fold it into the center of the omelette. Repeat with the other side. Slide the folded Omelette onto a plate.