Add all the ingredients listed under "Honey Garlic Stir-Fry Sauce" in a medium bowl, whisk to combine. Set aside.
Place a large cast iron skillet or stir-fry wok over medium-high heat and once hot add the oil. Wait for the oil to heat up.
Next, add the chopped broccoli florets, bell peppers, and mushrooms. Stir and cook for 5-7 minutes, or until the veggies are tender. Remove from pan to a plate.
Season chicken lightly with salt and pepper. Add the cubed chicken to the same pan. Stir and cook for about 7 minutes (about 3 minutes on each side) or until the chicken is golden-brown and cooked through.
Once the chicken has been cooked, add back the veggies. Give the sauce a stir and add it to the pan.
Stir and cook everything for another 5 minutes, until the sauce thickens and the chicken and veggies are well coated in it.
Tip: if the sauce is too thin, mix in a bowl 1 tablespoon of cornstarch with 2 tablespoons of water until fully dissolved and add the mixture to the pan. Cook for a few minutes. Repeat if needed.
Garnish with chopped green onions and sesame seeds.