In a large bowl, whisk together the soy sauce, brown sugar, rice vinegar, chili garlic paste, ginger, garlic, and sesame oil. Add the cornstarch and beef stock to the sauce and stir until smooth.
Heat a large wok or skillet over medium high heat and add 1 tablespoon of cooking oil and add the carrots. cook for 2-3 minutes until starting to soften then add the rest of the vegetables and cook for an additional few minutes until tender-crisp, about 3 minutes. Pour the sauce mixture into the skillet and bring to a boil. Cook and stir for 2 minutes until it begins to thicken. Serve with rice and a sprinkle of sesame seeds if desired.