Slice the steak very thinly, cutting against the grain. This will make it more tender.
Brown the steak in a pan on medium high heat, adding salt and pepper to taste.
At the same time saute peppers and onion in butter till tender.
Add 2 eggs to a bowl with salt and pepper and whisk till blended.
Heat non-stick skillet on medium high heat and add butter.
Once butter has stopped foaming add eggs to the skillet and stir quickly with a spatula for 5 seconds then rotate and tilt the pan to allow any liquid on the top to run off the side to cook.
Let the omelette finish cooking with no movement.
Add the cheese to the omelette and about ⅓ cup of steak and pepper filling per omelette.
Fold the omelette and slide onto a plate to serve.
Continue working in batches until all omelettes have been made.
Notes
Par-freezing the steak allows you to cut it easier. I recommend using a mandolin.