Preheat oven to 400 degrees F.
Cook the rice according to package directions.
Spread cauliflower and broccoli on one baking sheet. Spread chickpeas and carrots on another baking sheet. Drizzle 1 tsp oil over each baking sheet and give veggies a toss. Sprinkle with salt and pepper.
Roast for 20-30 minutes, turning the pans and giving them a shake every ten minutes. Cauliflower and broccoli takes about 30 minutes, carrots and chickpeas take about 20, so start the broccoli/cauliflower first and put the chickpeas/carrots in after the first 10 minutes. (Every oven is different, so keep an eye on everything to make sure you don't burn them.)
Combine all dressing ingredients in a small bowl or cup and whisk until smooth. Add more water, as needed, to thin. Set aside.
When veggies and chickpeas are done, make your bowls! A little rice, broccoli, cauliflower, carrots, chickpeas, sesame seeds and dressing in each individual bowl.