Place all the sauce ingredients in a blender. Cover and blend until well combined, about 20 seconds. Set aside.
To a gallon Ziploc bag, add the chicken cubes, 2 tablespoons of the sauce, and the cornstarch. Seal the bag and toss to evenly coat, set aside.
In a large skillet, heat 1 tablespoon olive oil over medium-high heat until it makes sizzling/popping sounds. Add the coated chicken and cook until it starts to brown and the juices run clear, about 6-9 minutes. (Make sure the chicken is cooked through before moving on.) Remove the chicken from the skillet and set aside.
Add 1 tablespoon of oil to the same skillet over medium-high heat. Gently add the broccoli and toss to coat, cooking for 1 minute. Add ¼ cup of water, cover the pan, and lower the heat to medium. Steam the broccoli for 2 minutes.
Remove the lid and push the broccoli to one side of the pan. Add 1 tablespoon of olive oil and add the red peppers, garlic, and ginger. Stir and cook for 1 minute. Add the chicken and remaining sauce to the skillet, stir to combine. Bring everything to a boil and cook 3-5 minutes, stirring constantly.
Remove from heat and top with green onions for garnish. Serve immediately with rice.