Heat 1 tablespoon of olive oil in a large skillet over medium heat. Add the onions and cook until softened, about 3 minutes. Add the mushrooms, green bell pepper, and red bell pepper. Cook until tender, about 5-7 minutes. Remove from the skillet and set aside.
Add the remaining tablespoon of olive oil to the skillet. Brown the shaved steak until just cooked through, careful not to over cook it.
Return the cooked vegetables to the skillet, stirring to combine with the steak.
Sprinkle shredded provolone over the mixture. Reduce heat to low, cover, and let the cheese melt for about 2 minutes.