Created by ellie on November 15, 2019
Step 1: Place steak on a plate and freeze until firm (30 minutes).
Step 2: In a saucepan over high heat bring the first 4 ingredients (soy sauce - mirin) to a simmer, stirring to dissolve the sugar. Reduce heat to medium and cook until reduced to 1/2 cup (3-5 minutes). Divide only between bowls and let cool. Cover 1 bowl with plastic wrap and set aside for serving.
Step 3: Place steak on a cutting board and starting at the narrow end slice steak 3/8 inch thick on the bias against the grain until the width of steak is 7 inches. Cut steak in half lengthwise and contuse to slice each half on the bias against the grain -- you should have 24 slices. Pound each slice between 2 sheets of plastic wrap to a thickness of 3/16th inch.
Step 4: Arrange 3 slices on a cutting board with short side of slices facing you (overlap slices by 1/4 inch and alternating tapered ends if necessary) to form a rectangle that measures 4 x 4 inches. Place 4 scallion halves along the edge of the rectangle nearest to the edge of the counter, with the white tips hanging over the edges of the steak on either side. Starting from the bottom edge and rolling away from you, roll into a tight cylinder. Insert 3 toothpicks into the end flaps and center of the roll. Transfer to a platter and repeat with remaining steak and scallions. (***rolls may be assembled and refrigerated up to 24 hours).
Step 5: Using a gas grill; turn all burners on high, cover and heat until grill is hot (15 minutes). Clean and oil grate and place rolls on grill and cook until first side is beginning to char (about 5 minutes), flip rolls and brush cooked side with glaze (made earlier) and cook another 5 minutes or so. Cook remaining 2 sides, glazing after each turn (about 20 minutes total cooking time). Transfer to a cutting board, tenting with foil and let rest for 5 minutes. Discard all remaining glaze.
Step 6: Remove picks from rolls and cut rolls crosswise into 3/4 inch pieces. Arrange rolls cut side down on serving plater and drizzle with 2 tablespoons reserved glaze, sprinkle with sesame seeds and serve passing remaining reserved glaze.