Preheat the broiler and, if you have an adjustable rack, make sure it is as close to the heat source as it can get.
Heat the oil in a small saucepan over medium heat. Add the ginger and garlic and cook, stirring, until you can really smell everything and the garlic turns golden, about 3 minutes. Add the soy sauce, brown sugar and red pepper flakes, if using. Increase the heat to medium-high and let the soy glaze simmer until slightly reduced and syrupy, stirring occasionally, about 5 minutes. Set the glaze aside to cool for about 5 minutes.
Season the flank steak lightly with black pepper. Brush the top side of the steak with some of the soy glaze, then broil it for 4 minutes. Using tongs, turn the steak, then brush the second side with the glaze. Broil the flank steak until it is done to your liking, about 4 minutes longer for medium-rare. Transfer the steak to a cutting board and let it sit for 5 minutes. Meanwhile, bring the remaining soy glaze to a simmer over low heat.
Thinly slice the flank steak across the grain and brush the slices with some of the reheated soy glaze. Transfer the sliced steak to a platter and scatter the green onions, if using, on top. Arrange the lime wedges on the edge of the platter for people to squeeze over their steak if they like. Put the rest of the soy glaze in a small pitcher or bowl to serve at the table for drizzling over rice.