Make the Teriyaki sauce: In a small pot, whisk together the soy sauce, rice vinegar, brown sugar, sesame oil, garlic and ginger together over medium-high heat until it starts to bubble. Mix the cornstarch and 1/4 cup water together in a small bowl, and then add to the pot, whisking until the sauce thickens slightly. Remove from heat and set aside.
Cook the noodles: Boil the noodles according to package instructions, this will vary depending on the kind of noodle you use. Drain and set aside.
Cook the vegetables: In the same pot you used to boil the noodles, add the broccoli, carrot and 1/2 cup of water. Turn the heat to high and cover, steaming for 3-4 minutes, until the vegetables have softened and most of the water is gone.
Turn off the heat and add the noodles and sauce to the pot with the vegetables. Stir to coat everything well. Serve sprinkled with sesame seeds, chopped green onions and hot sauce, as desired. Enjoy!