Wash hands with soap and water.
Rinse the broccoli florets and garlic cloves under cold running water. Gently scrub the carrots, yellow and red bell pepper, and fresh ginger with a clean vegetable brush under running water. Dry with a clean towel.
Thinly slice carrots, red and yellow bell pepper, and set aside. Finely mince the ginger and cloves, and set aside.
In a small bowl, prepare the sauce by whisking together the cornstarch and water. Add the remaining sauce ingredients and whisk to combine. Set aside.
On a separate cutting board, cut the chicken into medium-sized chunks. Do not rinse raw chicken.
Wash hands with soap and water after handling raw chicken.
In a large skillet or wok over medium-high heat, add 1 Tablespoon olive oil.
Season the chicken with salt and pepper and add to the skillet. Wash cutting board, counter, and utensils after handling raw chicken. Wash hands with soap and water.
Cook until the chicken reaches 165 °F on a food thermometer, about 3 to 5 minutes. Using a clean plate, remove the chicken from the pan and set it aside.
Reduce heat to medium and add the remaining 1 Tablespoon of oil to the skillet.
Add the broccoli, carrots, yellow bell pepper and red bell pepper. Stir constantly until crisp-tender, about 3 to 5 minutes.
Add the ginger and garlic. Cook for 1 minute, stirring constantly.
Add the chicken back into the skillet and mix well.
Push the ingredients to the side of the pan and whisk in the sauce.
Mix all the ingredients together until well combined. Bring to a low boil and cook for at least 1 to 2 minutes to allow the sauce to thicken.
Serve over brown rice.