Heat one tablespoon of salted butter in a non-stick pan over medium heat.

When the butter is bubbly, swirl it around the pan. Then, pour the beaten eggs into the pan and swirl again to distribute them evenly.

Reduce the heat and watch the egg cook until you can lift it and see that the bottom is golden brown and the top is mostly set.

Add the broccoli, onion, and cheese, and fold the omelette in half. Do not flip it.

Cover the pan with a lid and reduce the heat to low until the egg is fully cooked.

Garnish the top with chopped dill and serve the omelette hot.