In a medium nonstick skillet over medium-high heat, melt the butter.
Add the onion, red bell pepper, green bell pepper, garlic, and ham. Saute until the ham is crisp, about 2 minutes.
In a small bowl, beat the eggs with the salt and pepper. Pour the eggs into the skillet with the vegetables and ham. Reduce the heat to medium.
Cook the eggs for 3 to 4 minutes. Flip the omelet over. After flipping, top one-half of the omelet with the Cheddar cheese.
After 1 to 2 minutes, fold the omelet over, covering the cheese. Cook for another 1 to 2 minutes, until the cheese melts.
Remove the omelet from the skillet to a plate, and serve.