In a mixing bowl, combine the soy sauce, brown sugar (or honey), Gochujang, rice vinegar, grated ginger, minced garlic, and toasted sesame oil. Whisk until the sugar is dissolved and the mixture is well combined. Set aside.
Bring a pot of water to a boil and cook the brown rice noodles according to package instructions. Drain and rinse under cold water to stop the cooking process. Toss with a little sesame oil to prevent sticking.
In a large skillet or wok, heat the sesame seed oil over medium-high heat. Add the carrots, bell peppers, and mushrooms. Stir-fry for about 3-4 minutes, until the vegetables are tender but still crisp.
Push the vegetables to one side of the skillet and add the sliced flank steak to the other side. Cook for about 3-4 minutes until the beef is browned and cooked through. Mix the beef with the vegetables.
Pour the sauce over the beef and vegetables. Stir well to coat everything evenly. Let it cook for another 1-2 minutes to heat through and allow the flavors to meld.
Add the cooked noodles to the skillet and toss everything together until the noodles are well coated in the sauce and mixed evenly with the beef and vegetables.
Remove from heat and sprinkle with chopped green onions, sesame seeds, and cilantro. Serve immediately and enjoy your 30-Minute Stir Fried Korean Beef and Toasted Sesame Noodles!