Cook the rice. If you are using rice, cook the rice according to package instructions, then place it to the side.
Cook the vegetables. Heat the sesame seed oil in the wok over medium-high heat. Add the baby corn, water chestnuts, broccoli florets, mushrooms, carrot, and pepper slices. Stir the vegetables and cook for 5-7 minutes until they have softened.
Add the stir fry sauce. Combine the vegetable broth, soy sauce, brown sugar, apple cider vinegar, garlic, red pepper flakes, and cornstarch in a small bowl and stir to combine. Add the stir fry sauce to the wok, then stir to coat the vegetables. Cook for another 2 minutes until the sauce has thickened, then remove the pan from the stove. Serve the vegetable stir fry over the rice. Mangia!