Whisk eggs, salt, and pepper together in a small bowl and set aside.
Melt butter in medium-size skillet; add ham and sautee until browned and crispy, approximately 2 minutes.
Add onions and peppers and sautee until onions become translucent, approximately 2-3 minutes. When cooked, transfer ham, onions & peppers into a clean bowl.
Add eggs to the same skillet, running a heat-proof spatula through the center to allow eggs to cook through.
When the center is still slightly runny, add the ham, onions, and peppers to the center and carefully fold omelet in half. Cook on one side for one minute, then flip to the other side until center is cooked through.