Arrange a rack in the middle of the oven and heat to 350°F.
Lay the flank steak flat on a cutting board, with the grain running left to right, and season both sides with salt and pepper. Spread the roasted red peppers evenly across the steak. Sprinkle the arugula on top, then crumble the gorgonzola evenly over the arugula.
Starting at the bottom of the steak, roll it up tightly, away from you. Place the steak roll seam-side down. Tie it tightly together with kitchen twine, spacing the ties about 1 1/2 inches apart. Use toothpicks to secure any spots that may seem loose. Cut the roll crosswise into 4 equal pieces.
Heat the oil in a large cast-iron skillet over high heat until shimmering. Add the steaks cut-side down and sear until the bottoms are well-browned, about 2 minutes. Flip and sear until the other side is well-browned, about 2 minutes more.
Transfer the skillet to the oven and bake until an instant-read thermometer registers 120°F for medium-rare or 130°F for medium, 10 to 15 minutes. Transfer the steak roll-ups to a plate and let rest for 5 minutes before removing the twine and toothpicks and serving.