Pat steak dry and place on rimmed baking sheet. For easier clean up, line the baking sheet with foil or parchment. Lightly score both sides of steak with the tip of a paring knife, making shallow parallel cuts (no deeper than an ⅛") about 1" apart and running across the grain of the meat (this will prevent the steak from curling as it cooks). Season generously all over with salt and pepper; let sit at room temperature at least 30 minutes and up to 1 hour.
Prepare grill for medium-high heat; lightly oil grate.
On another baking sheet lined with foil or parchment (once again, for easier clean up) toss scallions with 2 Tbsp. olive oil to coat; season with salt and pepper.
Spray grill with non-stick oil. Grill scallions, turning often, until tender and charred in spots, about 1-2 minutes. Return to same baking sheet and cut off bottom-bulb part, if desired.
Pat steak dry again (the salt will have drawn out more moisture) and rub with remaining 1 Tbsp. olive oil.
Re-spray grill with non-stick oil. Grill steak for 8-10 minutes total. 4-5 minutes per side, until browned and with grill marks. Steak will be medium-rare. (For more well done meat, cook for an additional 5 or so minutes.) Transfer to cutting board and let rest 10–15 minutes.
Thinly slice steak crosswise (against the grain) and arrange on a rimmed platter; drizzle all of the juices that have collected on the cutting board over the steak. Arrange grilled scallions on top, then pour sauce over. Let sit at least 15 minutes and up to 1 hour before serving. To serve, sprinkle with sesame seeds as desired.