Preheat a panini press or griddle. Bring a large pot of water to a boil. Add the broccoli rabe and cook until bright green, about 3 minutes. Drain well.
In a large skillet, heat the 1/4 cup of oil. Add the minced garlic, anchovy paste and crushed red pepper and cook over moderately high heat for 10 seconds. Add the broccoli rabe and season with salt. Cover and cook over moderately high heat, stirring occasionally, until the broccoli rabe is tender, about 5 minutes.
Layer 2 slices of provolone on the bottom of each roll. Top with the broccoli rabe, roast beef, Peppadews and the remaining provolone. Close the rolls and brush lightly with oil. Grill the sandwiches until toasted and the cheese is melted, about 7 minutes. Serve hot.