Place steak in the freezer for about 20 minutes so you can cut it easily. Once partially frozen, using a very sharp knife, slice steak into very thin slices, almost shaved. Cut into smaller pieces. Season with salt and pepper.
Heat a large skillet over a medium-high heat. Add a little bit of olive oil to the pan and add steak, cook until browned and cooked through. If needed, chop into smaller pieces.
Add 2 teaspoons of olive oil to a small saucepan set over a medium heat Add onions and green pepper. Sweat until they start to soften, about two minutes. Add steak, cheeses, ½ & ½ and chicken stock.
Stir until cheese melts and mixture becomes homogenous. If needed add mor half & half to loosen the sauce up.