Boil pasta: Bring a large pot of salted water to boil. Cook linguine according to package directions until al dente. Drain but do not rinse. Set aside.
Brown the beef: Heat large skillet over medium-high heat. Add ground beef and cook, breaking into small pieces, until browned and cooked through, about 5 to 7 minutes. Drain all but 1 tablespoon of fat.
Add aromatics: Add minced garlic to beef and cook for 30 seconds until fragrant. Stir in brown sugar and let it melt slightly, about 30 seconds.
Create sauce: Add beef broth, soy sauce, hoisin sauce, ground ginger, black pepper, and red pepper flakes if using. Stir well and bring to a gentle simmer.
Thicken sauce: In a small bowl, mix cornstarch with cold water until smooth. Pour into simmering sauce while stirring constantly. Cook for 2 to 3 minutes until sauce thickens and becomes glossy.
Combine and serve: Add drained linguine to the skillet. Toss with tongs until every noodle is coated in sauce. Garnish with sliced green onions and serve immediately.
