Add one tablespoon butter and diced ham to a large non-stick skillet and set over medium-low heat. Cook, stirring occasionally, until the ham develops some color and is heated through, approximately 6-8 minutes.

Transfer the ham to a small plate and set aside. Return the skillet to the cooktop and reduce heat to low.

Whisk together the eggs, milk, salt, and black pepper in a medium bowl. Set aside.

Add the remaining butter to the skillet and swirl to coat the bottom as it melts. Pour in the egg mixture and tip the skillet in each direction to create an even layer.

Tip: Before the egg mixture fully “sets,” push the edges back with a spatula and again tip the skillet in each direction to allow more of the egg mixture to contact the hot surface.

Once the egg starts to set, add the ham and shredded cheddar cheese evenly across the surface. Partially cover the skillet with a lid until the cheese starts to melt and the egg is mostly cooked through, approximately 2-3 minutes.

Remove the lid and carefully flip half the omelet on top of the other half with a spatula. Cover and cook for an additional minute or two to ensure the omelet is cooked through and the cheese is completely melted.

Remove from heat and cut the omelet in half with a plastic spatula. Transfer to serving plates and garnish with a couple sliced tomatoes and sprigs of fresh basil, if desired, before serving. Enjoy!