In a medium bowl, whisk together the eggs, liquid (if using), and salt. Whisk the eggs in a side-to-side motion until uniform in appearance, do not over mix. Set aside.
In an 8-inch nonstick skillet, heat 1 teaspoon butter over medium heat until it just begins to bubble and foam, but does not brown. Add the diced ham, saute until lightly browned, 1 ½ to 2 minutes.
Add the diced onions, green and red bell pepper, saute until crisp-tender, about 2 minutes. Transfer ham and vegetables to a bowl. Wipe out the pan with a paper towel.
In the clean pan, heat 1 teaspoon butter over medium-high heat until it just begins to bubble and foam, but does not brown.
Add the eggs to the pan, use a spatula to immediately pull the cooked curds from the edges of the pan toward the center, allowing the raw egg to run underneath, tilting the pan to help move it to the bottom of the pan. Start from the top of the pan, and work around to create curds around the entire omelet, about 45 to 60 seconds.
Once the eggs are mostly cooked, similar to soft scrambled eggs with a glossy and slightly wet surface, turn the heat down to low.
Add the ham and vegetables to one half of the omelet, then sprinkle on the cheddar cheese. Turn off the heat and move the pan to a cool part of the stove, cover the omelet and allow it to finish cooking, about 1 to 2 minutes.
Using a spatula, fold the other half of the omelet on top. The surface will be lightly golden brown.
Transfer omelet to a plate and garnish with pepper and chives. Serve immediately.
For a less browned surface on the omelet, use medium instead of medium-high heat.
I use ham steak to give nice chunks of meat, but ham slices will also work.