Place 1 Tablespoon of butter in a skillet over medium heat.

Once butter is melted, add the ham and cook until lightly browned, about 3-4 minutes.

Add the diced onion and peppers and continue to cook until onions are translucent, about 3 minutes.

Season the veggies and ham before removing to a clean plate.

Wipe out the skillet and add the remaining butter.

In a small bowl, whisk together the eggs and milk for 1 minute until light and frothy.

Once the butter is melted, pour in the egg mixture.

As the eggs cook, use a spatula to clean the edges of the eggs of the omelette. Jiggle the pan around to evenly distribute the eggs and ensure they cook fully.

Once the egg is no longer liquid, but still soft, sprinkle on the shredded cheese and place a large lid over the skillet to encourage the cheese to melt, about 1 minute.

Scoop the vegetables and ham mixture onto half of the omelette and then use a spatula to fold the empty half of the omlette overtop.

Continue to cook until omelette is well-browned on both sides, as desired.