Step 1

Heat vegetable oil in a small saucepan over medium-high heat until shimmering (a scingle scallion dropped into it should sizzle immediately. Meanwhile, combine scallions and ginger in a medium bowl and season well with salt. When oil is hot, pour over scallions and ginger. It should sizzle for a few seconds. Allow to cool.

Step 2

Lay steak on a cutting board with grain running parallel to the edge of the counter. Trim left and right edges to form a clean rectangle and reserve scraps for another use. Hold steak flat with your non-knife hand and, with a sharp boning knife, carefully butterfly the steak, leaving the back edge attached by 1/2- to 1/4-inch of meat. Open up steak and flatten the seam gently with your hand to form a large perfect rectangle.

Step 3

Season steak on exposed side with salt and pepper. Spread scallion-ginger mixture over steak, leaving a 1-inch border at the top and the bottom.

Step 4

Carefully roll the steak away from you (the grain should run width-wise), tightening as you go until it is rolled into a cylinder. Let it rest with its seam-side down.

Step 5

Tie the beef tightly with twine, spacing the ties evenly every 1 1/2 inches. Insert a skewer through each piece of twine. Using a sharp knife, carefully cut between the ties to make the pinwheels. Season with salt and pepper.

Step 6

To Finish on the Grill: Light one chimney full of charcoal. When all the charcoal is lit and covered with gray ash, pour out and spread the coals evenly over half of coal grate. Alternatively, set half the burners of a gas grill to high heat. Set cooking grate in place, cover grill and allow to preheat for 5 minutes. Clean and oil the grilling grate. Place the pinwheels on the hot side of the grill and cook without moving until well charred on first side, about 3 minutes. Flip steaks and char second side, about 3 minutes longer. Transfer to cooler side of grill, brush with 1 to 2 tablespoons teriyaki sauce, cover, and cook until an instant read thermometer inserted into the center registers 120°F for medium-rare or 130°F for medium, flipping once half way through cooking and brushing with more sauce. Transfer to a platter, let rest for five minutes, brush with more sauce, sprinkle with scallions, and serve.

Step 7

Alternatively, to Finish Indoors: Adjust oven rack to center position and preheat oven to 400°F. Heat 2 teaspoons vegetable oil in a large skillet over high heat until lightly smoking. Add steaks and cook, turning occasionally, until well browned on both sides, about 4 minutes total. Transfer to a wire rack set in a foil-lined rimmed baking sheet. Brush with sauce and transfer to oven. Cook until an instant read thermometer inserted into the center registers 120°F for medium-rare or 130°F for medium, flipping once half way through cooking and brushing with more sauce, about 2 to 5 minutes total. Transfer to a platter, let rest for five minutes, brush with more sauce, sprinkle with scallions, and serve.