Fill a large pot with water and bring to a high boil. Do not salt the water.
Place skillet over medium-high heat. Add ground beef and cook for 6 minutes, letting it sit to develop a brown crust before breaking it up. During the last 2 minutes, add minced ginger and garlic. Cook until beef is fully browned with no pink remaining (about 8 minutes total).
Once water is boiling, add linguine and cook according to package directions (usually 9-11 minutes) until al dente. Set a timer. When done, drain noodles and set aside.
Carefully drain excess fat from the cooked beef. Return drained beef to skillet over medium heat.
Add soy sauce, beef broth, brown sugar, red pepper flakes, black pepper, and hoisin sauce to the beef. Stir together until brown sugar begins dissolving and sauce bubbles gently.
In a small bowl, mix cornstarch and water together until cornstarch completely dissolves. Pour into beef mixture and stir constantly. Bring to a gentle boil until sauce thickens and coats the back of a spoon (1-2 minutes).
Add drained noodles to the skillet. Use tongs or wooden spoons to toss everything together for 2 minutes, ensuring every strand gets coated in the sauce.
Turn off heat and let noodles rest in sauce for 3-4 minutes to absorb flavors.
Transfer to serving bowls and scatter sliced green onions over the top. Add sesame seeds if desired.