Bring a large pot of salted water to a boil and cook linguine according to package instructions. Drain and set aside.
Heat a large skillet over medium-high heat and brown the ground beef until fully cooked. Drain excess fat if needed.
Add minced garlic and cook for about 1 minute until fragrant.
Stir in soy sauce, beef broth, brown sugar, hoisin sauce, ginger, black pepper, and red pepper flakes.
Mix cornstarch with water, add to the skillet, and bring to a gentle boil until the sauce thickens.
Add cooked noodles and toss well to coat. Let the Mongolian Ground Beef Noodles sit for 2–3 minutes to absorb the sauce.
Garnish with green onions and serve warm.