Whisk all sauce ingredients together in a small bowl. Cover and refrigerate.
Heat 1 tablespoon oil in a large skillet over medium heat. Cook the onion and bell pepper with a pinch of salt for 8 to 10 minutes, until softened and golden. Transfer to a bowl.
Increase heat to medium-high, add the remaining oil, and cook the shaved steak 3 to 4 minutes, breaking it apart, until no pink remains. Season with Worcestershire, garlic powder, onion powder, salt, and pepper. Drain off excess liquid.
Return the vegetables to the pan, turn off the heat, and stir in the cream cheese until melted. Add the provolone and stir until just beginning to melt. Spread on a sheet pan and cool at least 15 minutes.
Place a wrapper in a diamond orientation. Add about 3 tablespoons of filling. Fold the bottom corner up and tuck, fold in the sides, moisten the top corner with water, and roll tightly to seal. Repeat with remaining wrappers.
Deep fry: 350°F for 3 to 4 minutes, turning once. Air fry: oil the rolls, 375°F for 8 to 10 minutes, flipping halfway. Bake: 425°F on a wire rack for 18 to 20 minutes, turning once.
Rest 2 minutes, slice on the diagonal, and serve hot with the horseradish sauce.