Prepare a medium-hot fire in a grill. Place a steel grill fry pan in the center of the grill and heat until smoking.
In a bowl, stir together the onion, bell peppers and 2 Tbs. of the olive oil, and season with smoked sea salt and pepper. Transfer the mixture to the fry pan. Cover the grill and cook, tossing the vegetables occasionally, until browned and softened, 8 to 10 minutes. Transfer to a bowl, cover with aluminum foil and place on the edge of the grill to keep warm. Return the fry pan to the grill.
In a bowl, stir together the steak and the remaining 2 Tbs. olive oil, and season with smoked sea salt and pepper. Working in 2 batches, place the beef in the fry pan, cover the grill and cook, tossing the beef occasionally, until browned, 4 to 5 minutes per batch. Return all the beef along with the vegetable mixture to the pan and stir to combine.