Light a grill or preheat a grill pan. In a small saucepan, heat the oil. Add the garlic and ginger and cook over moderately high heat, stirring occasionally, until the garlic begins to turn golden. Add the soy sauce, sugar and crushed red pepper and cook, stirring, until syrupy, about 3 minutes; let cool.
Season the steak with salt and pepper. Grill the steak for 10 minutes for medium-rare meat, turning once; during the last minute, brush all but 2 tablespoons of the glaze over the steak. Transfer the steak to a cutting board and let stand for 5 minutes.
Thinly slice the steak and brush with the reserved 2 tablespoons of glaze. Transfer to a platter, sprinkle with scallions and serve with lime wedges.