Cook the linguine according to package instructions until al dente. Drain and set aside.
In a large skillet over medium heat, cook the ground beef until browned. Drain excess fat.
Add minced garlic to the skillet, cooking until fragrant. Stir in brown sugar, beef broth, soy sauce, hoisin sauce, ginger, black pepper, and optional red pepper flakes; mix thoroughly.
In a small bowl, whisk together cornstarch with water until smooth. Pour this mixture into the skillet while stirring continuously until it thickens, about 2-3 minutes.
Add the cooked linguine to the skillet and toss gently until well coated in the sauce.
Garnish with sliced green onions before serving hot.