Heat 2 tsps cooking oil in a wok over medium-high heat.
When oil is hot, add in carrots, zucchini, and mushrooms. Stir fry for 1-2 minutes until the veggies start to brown. Add in red bell peppers and stir fry an additional minute.
Remove veggies from wok.
Return wok to heat, and add 2 tsps cooking oil and heat
Once oil is heated, add in 8 ounces of finely sliced chicken, season with salt and pepper, and stir fry for 1 minute. Flip chicken over and stir fry an additional minute.
Pour stir fry sauce in over chicken and turn heat up to high.
When sauce starts bubbling and thickening, add veggies back in, as well as remaining vegetables (broccoli and snow peas)
Stir to coat everything in sauce, and cook until broccoli is crisp tender, and additional 2 minutes or so.
Serve over white rice, garnish with sesame seeds and green onion.