In a medium-sized mixing bowl, beat the eggs and olive oil together.
Heat up a medium-sized pan to medium heat. Pour half the egg mix into the pan and cover.
Once the omelette is solid, use a spatula to slide the egg onto a plate or paper towel. Repeat with the rest of the egg mixture.
In the same skillet, add the second half of the olive oil along with peppers and onion. Sauté on medium heat until the vegetables begin to soften. Transfer to a bowl and set aside.
Add the shredded steak to the skillet and sauté over medium-high heat until cooked.
Fill the omelettes by layering half of the thinly sliced provolone into each eggshell and topping with the hot meat and sautéed vegetables.
Roll the omelettes and place back in the skillet on medium then cover to melt the cheese.
