Heat 1 tablespoon of olive oil in a large skillet over medium-high heat.
Season the chicken cubes with salt and pepper, then add them to the skillet. Cook until the chicken is browned and fully cooked, about 6-7 minutes. Remove the chicken from the skillet and set aside.
In the same skillet, add the remaining 1 tablespoon of olive oil. Add the broccoli florets and stir-fry for 3-4 minutes until bright green and tender-crisp.
In a small mixing bowl, whisk together honey, soy sauce, apple cider vinegar, and minced garlic.
Return the cooked chicken to the skillet with the broccoli. Pour the honey garlic sauce over the chicken and broccoli mixture.
Bring the sauce to a simmer over medium heat. Once simmering, stir the cornstarch mixture into the sauce to thicken it, cooking for about 1-2 minutes.
Toss the chicken and broccoli in the thickened sauce until well coated.
Serve the honey garlic chicken and broccoli over cooked rice, sprinkled with toasted sesame seeds if desired.
