Step 1

Whisk honey, soy sauce (or tamari), garlic, vinegar and crushed red pepper in a small bowl. Place chicken and half of the honey mixture (about 1/4 cup) in a zip-top plastic bag; remove excess air and seal bag. Massage the chicken in the sealed bag until well coated. Refrigerate for at least 30 minutes and up to 2 hours. Reserve the remaining honey mixture.

Step 2

Preheat oven to 400 degrees F. Line a large rimmed baking sheet with foil; coat with cooking spray. Remove the chicken from the marinade (discard marinade); arrange on 1 side of the prepared pan. Combine carrots and 1 tablespoon oil in a medium bowl; toss well to coat. Spread the carrots in an even layer on the other side of the pan. Bake the chicken and carrots for 15 minutes. Remove from the oven; stir the carrots.

Step 3

Combine broccoli and the remaining 1 tablespoon oil; toss well to coat. Distribute the broccoli evenly over the chicken and carrots on the pan. Sprinkle salt and pepper over all. Bake until the vegetables are tender and a thermometer inserted in the thickest portion of the chicken registers 165 degrees F, 15 to 18 minutes.

Step 4

Meanwhile, whisk cornstarch and water in a small bowl until no clumps remain. Combine the cornstarch mixture and the reserved honey mixture in a small saucepan; bring to a simmer over medium-low heat, whisking once or twice. Simmer, whisking often, until the sauce is clear and thickened, about 2 minutes. Drizzle over the chicken and vegetables. Serve hot.