In a small bowl, whisk together the cornstarch, chicken broth, soy sauce, and honey until smooth. Set this bowl aside while you work on the chicken and vegetables. Whisking it early means it's ready to pour in the moment you need it, so the sauce doesn't slow you down later in the process.
Heat a tablespoon of olive oil in a large skillet over medium-high heat. Add the diced chicken and season it with salt and pepper right in the pan. Cook for three to five minutes, stirring occasionally, until the pieces are browned on the outside and cooked through, then move them to a separate plate.
Add the remaining olive oil to the same skillet and toss in the broccoli, bell peppers, and shredded carrots. Stir them occasionally so they cook evenly, and let them go until they're tender but still have a little bite left. This usually takes about four to five minutes over medium-high heat.
Stir the minced garlic and ground ginger into the vegetables and let them cook for another minute or two. You'll know they're ready once the garlic smells fragrant and toasty rather than raw. Keep an eye on it here, since garlic can burn quickly if you walk away.
Add the cooked chicken back into the skillet with the vegetables. Pour the stir fry sauce over the top and stir everything together so the chicken and vegetables are evenly coated. Bring the mixture to a boil and let it bubble for about a minute so the sauce thickens up.
Sprinkle sesame seeds over the top of the finished stir fry for a bit of crunch and a nice presentation. Serve it right out of the skillet on its own, or spoon it over a bowl of rice or noodles. I like to give it a final taste and adjust the salt and pepper before bringing it to the table.