Crack eggs into small bowl and beat well. Set aside.
Heat non-stick skillet over medium heat. When hot, add coconut oil to pan.
Pour half of the beaten eggs into the skillet and coat the bottom of the pan. When the egg has partially set, scrape the edges and tip the pan so that the uncooked egg at the top can spread to the hot cooking surface of the skillet.
Immediately after, add half of the vegetables and ham to one half of the omelet and continue to cook until the egg is almost fully set.
Using a spatula, fold the empty half over top of the ham and veggies. Cook for 2 minutes longer, then serve.
Repeat the process with the remaining ingredients to make the second omelet.