In an omellete pan over medium heat, drizzle in olive oil and melt butter. Then add the onions.
Once onions are transparent - about 5 minutes - add ham. Simmer ham until crispy - about 5 minutes.
Then add in your remaining vegetable ingredients - whatever amount you want.
In a bowl, scramble 2 eggs.
Add the eggs to the pan.
After a couple minutes when sides are firm, gently lift the side and tilt the pan so the egg pours underneath. This is important if you don't want a runny omelette.
Once the majority of the runniness is gone, add salt & pepper, and whatever your cheese preference.
Gently fold the omelette in half with your spatula, and let rest in pan on low heat for a minute.
Slide from the pan onto a plate.