Bring a large pot of salted water to a boil. Cook linguine noodles according to package directions until al dente. Drain and set aside.
Heat a large skillet over medium-high heat with vegetable oil. Add ground beef and cook for 2 to 3 minutes undisturbed, then break up and continue cooking until browned, about 7 minutes total. Drain excess fat, leaving about 1 tablespoon.
Push the beef to the sides and add minced garlic and ginger to the center. Cook for 30 seconds until fragrant, then mix with the beef.
In a bowl, whisk together soy sauce, brown sugar, beef broth, and hoisin sauce. Pour over the beef and stir well. Simmer for 2 minutes.
Mix cornstarch with 2 tablespoons water until smooth. Pour into the skillet while stirring constantly. Cook for 1 minute until sauce thickens and becomes glossy.
Add the cooked noodles to the skillet and toss until completely coated in sauce.
Serve immediately topped with sliced green onions and sesame seeds if desired.