Begin by bringing a large pot of salted water to a rolling boil over high heat. Add your choice of noodles and cook them according to package instructions until al dente, about 6–8 minutes.

In a large skillet or wok, heat 1 tablespoon of oil over medium-high heat. Add the ground beef and sauté for about 5-7 minutes until browned.

Stir in the minced garlic and grated ginger and sauté for about 1 minute until fragrant, making sure not to burn.

Pour in the soy sauce, brown sugar, and beef broth, stirring well. If using, add hoisin sauce. Simmer for 2-3 minutes.

Add the mixed vegetables and cook for an additional 2-3 minutes until tender but still vibrant.

Mix the cornstarch with water to form a slurry and pour it into the skillet. Stir until the sauce thickens, about 1-2 minutes.

Add the drained noodles to the skillet, tossing them with the sauce and beef mixture until well-coated.

Drizzle with sesame oil and garnish with sliced green onions and red pepper flakes if desired. Serve hot.