Bring a large pot of salted water to a boil and cook the linguine according to package directions until al dente, usually 8-10 minutes. Drain in a colander and set aside without rinsing; the starch helps the sauce cling better. Start browning your beef while the pasta finishes cooking to save time.

Heat a large 12-inch skillet over medium heat. Add the ground beef, breaking it apart with a wooden spoon. Cook for 5-7 minutes until the beef is completely browned with no pink remaining. Drain any excess fat by carefully tilting the pan and spooning it out.

Add the minced garlic to the browned beef and cook for about 1 minute, stirring constantly until fragrant and just starting to turn golden. Watch carefully to prevent burning.

Stir in the brown sugar, beef broth, soy sauce, hoisin sauce, ground ginger, black pepper, and red pepper flakes if using. Mix everything together thoroughly, scraping up any flavorful bits stuck to the bottom of the pan. Let this simmer for 2 minutes so the flavors can blend.

In a small bowl, whisk together the cornstarch and water until completely smooth with no lumps. Pour this slurry into the skillet and stir continuously for 2-3 minutes until the sauce thickens and becomes glossy, coating the back of your spoon.

Add the cooked linguine directly to the skillet and use tongs to toss everything together until every strand is coated in the sauce, about 1-2 minutes. Garnish generously with sliced green onions and serve immediately while hot.