Whisk the corn starch and cold water in a medium bowl until completely smooth, then whisk in the chicken broth, soy sauce, honey, toasted sesame oil, and crushed red pepper flakes. The mixture should look even and pourable, with no dry cornstarch clumps at the bottom of the bowl.
Heat 1 tablespoon of olive oil in a large skillet or wok over medium-high heat. The oil should shimmer across the pan before the chicken goes in.
Season the chicken with salt and pepper, then add it in batches if needed and cook for 3 to 5 minutes. Leave the pieces undisturbed for the first minute so they develop golden color instead of releasing moisture and steaming.
Move the cooked chicken to a plate and lower the heat to medium, then add the remaining 1 tablespoon of olive oil. The pan should remain hot but no longer aggressively smoking.
Add the broccoli, bell peppers, and carrots and cook, stirring occasionally, until crisp-tender. The broccoli will turn brighter green, and the peppers should soften slightly while still holding their shape.
Stir in the ginger and garlic and cook for 1 minute. A warm, fragrant aroma should bloom quickly without the garlic turning brown.
Return the chicken to the skillet and fold it through the vegetables. Distribute the chicken evenly so every piece can catch some of the sauce.
Whisk the sauce once more, pour it into the skillet, and stir gently to coat everything. The liquid will begin bubbling around the vegetables almost immediately.
Bring the sauce to a boil and cook for 1 minute, stirring occasionally. The sauce should turn glossy and lightly coat a spoon as it thickens.
Serve with rice and/or chow mein if desired. The warm grains or noodles catch the extra honey soy glaze.