Cook the crinkle-cut fries according to the package directions — bake or fry until golden and crispy, then keep warm.
Heat the oil in a skillet over medium heat. Add the chopped onion and green pepper and sauté, stirring occasionally, until softened and beginning to brown, about 6–8 minutes. Transfer the vegetables to a plate.
Increase the heat to medium-high and add the shaved beef to the same skillet. Cook, stirring and breaking up any larger pieces, until the meat is browned and cooked through, about 6–10 minutes. Season with salt and pepper, then remove from the heat.
Warm the Cheez Whiz in a small saucepan over low heat, stirring until smooth and pourable, or heat in short bursts in the microwave until soft enough to drizzle.
Arrange the cooked fries on a large platter or individual bowls. Top with the sautéed peppers and onions, then the cooked steak. Drizzle the warm cheese sauce over everything and serve immediately while hot.