Gently beat the eggs and 1/2 of the olive oil in a large bowl.
Heat a nonstick square pan, or skillet, over medium heat. Pour half of the egg mixture into the pan and cover until the egg is cooked through.
Once the omelet is solid, use a rubber spatula to release the edges and 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 until the vegetables begin to soften, and the onions caramelize. Transfer to a bowl and set aside.
Season the beef with the salt and pepper.
Add the meat to the hot skillet and sauté over medium high heat until cooked through. Toss the peppers and onion back into the hot skillet to warm them if needed.
Fill the omelets by layering half of the thinly sliced provolone into each eggshell and topping with the hot meat and sautéed vegetables.
Roll the omelets and place back in the skillet on medium then cover to melt the cheese. Serve hot!