Have a bowl of ice water large enough to hold the scallions at the ready.

In a large saucepan of salted boiling water, cook the lighter scallion ends for 1 minute, then add the darker green scallion ends and cook for 1 minute longer. Drain and transfer to the ice bath to cool, then drain and transfer scallions to a clean kitchen towel. Set aside while you prepare the steak.

In a medium bowl whisk the soy sauce, mirin, sake and sugar till the sugar is dissolved.

Place the steak on a cutting board with the grain running horizontally. Cut the steak crosswise (against the grain) into 4 equal pieces, then cut those pieces in half crosswise for a total of 8 pieces.

Butterfly each piece by slicing it horizontally through the middle almost all the way through, and then opening it up like a book.

Return the steak to your worksurface and transfer the marinade to a small saucepan. Simmer over medium low heat till thickened, about 10 - 15 minutes.

Meanwhile heat a tablespoon of vegetable oil in a large skillet over medium high heat (alternatively you can use a grill, grill pan or broiler).

Cook the negimaki, turning occasionally, until nicely charred and cooked through, about 12 minutes. Remove the pan from the heat and brush the rolls with the reduced marinade. Transfer to a cutting board, remove the toothpicks and cut into bite-sized pieces.

Arrange on a serving platter, drizzle with any remaining glaze and sprinkle with sesame seeds if using. Serve immediately.