You could just make your omlette “Italian style” (at least, that’s what style I’m told I most often make) and not try to fold it at all. Put a lid on the eggs about halfway through, and turn the heat down, add the veggies at this point. The eggs should be cooked on the bottom, but just starting to congeal in the middle. It’s still fluffy, and yummy, and technically, an omelette. 