Heat 1 Tbsp olive oil in a saucepan over medium heat. Add chicken and cook until just browned, about 3 minutes.
Add carrots, broccoli and mushrooms and cook for 2 more minutes.
In a small bowl combine the rest of the ingredients. Pour over the chicken and veggies and cook, stirring constantly until the sauce has reduced and thickened and the chicken is completely done.
Serve over noodles or rice and sprinkle with sesame seeds.