To a large skillet, add the olive oil and sesame oil, then heat them over medium-high heat. Once the oils are shimmering, add the chicken pieces. Cook for about 5 minutes, stirring occasionally to ensure even cooking. Look for the chicken to turn golden brown and be nearly cooked through.
While the chicken is cooking, prepare the cornstarch slurry. In a small bowl, combine the cornstarch and cold water. Stir until the cornstarch is completely dissolved. Set this aside for later use.
In a separate medium saucepan, combine the brown sugar, soy sauce, honey, hoisin sauce, chili garlic sauce, and ground ginger. Stir to combine and bring the mixture to a gentle boil over medium heat. You’ll want to see bubbles forming, indicating it’s cooking.
Once boiling, add the prepared cornstarch slurry to the saucepan. Whisk continuously for about 2 to 3 minutes, until the sauce thickens. It should become glossy and rich in color.
Push the cooked chicken to one side of the skillet. On the other side, add the broccoli florets. Pour the thickened sauce evenly over both the chicken and broccoli, then gently stir to combine. Make sure everything is well-coated in the sauce.
Cover the skillet and let it cook for another 5 minutes. This allows the broccoli to become crisp-tender. You can check for doneness by piercing the broccoli with a fork; it should be bright green and tender-crisp.
If desired, season the dish with salt and pepper to taste. Sprinkle some sesame seeds on top for garnish, enhancing both flavor and presentation.
Serve the Skinny Sesame Chicken and Broccoli immediately, either on its own or over a bed of rice for a heartier meal. Enjoy!