Cook the rice ahead of time and chill in the refrigrator or use leftover rice.
Heat a large skillet over medium heat adding the broccoli, cauliflower, and carrots to the skillet along with 2-3 tbsp water. Saute the vegetables until they are fork tender.
While the vegetables are cooking mix all of the sauce ingredients in a bowl.
Add the peas, corn, and rice to the skillet. Mix in the sauce.
Cook until the rice is tender and hot, about 10 minutes, stirring frequently.