Heat another drizzle of oil in same pan over medium-high heat. Add garlic and ginger and cook until fragrant, 30 seconds. Add beef, breaking up meat into pieces. Cook, tossing occasionally, until no longer pink, about 4 minutes. Increase heat to high and continue cooking until browned and crisp, about 3 minutes. Pour in remaining soy sauce and cook, tossing, until mostly evaporated, 1-2 minutes. Season with salt and pepper.