Preheat and prep the pan: Heat the oven to 425°F (220°C). Line a large sheet pan with parchment for easy cleanup.
Make the marinade: In a bowl, whisk balsamic vinegar, soy sauce, honey, garlic, Dijon, Italian seasoning, smoked paprika, 1 tablespoon olive oil, and a pinch of salt and pepper.
Marinate the chicken: Place chicken breasts in a zip-top bag or shallow dish.
Pour over half the marinade, coat well, and let sit for 15–30 minutes at room temp (or up to 8 hours in the fridge).
Season the veggies: In a large bowl, toss broccoli, peppers, red onion, tomatoes, and zucchini with remaining 1 tablespoon olive oil, a generous pinch of salt, and pepper. Add the remaining half of the marinade and toss again until lightly coated.
Arrange on the pan: Spread veggies in an even layer on the sheet pan, leaving space in the center for the chicken. Place marinated chicken breasts in the center, shaking off excess marinade to avoid pooling.
Roast: Bake for 18–22 minutes, flipping the chicken once halfway through.
Chicken is done when the thickest part reaches 165°F (74°C).
Optional broil: For extra caramelization, broil the pan for 2–3 minutes at the end. Watch closely so the honey doesn’t burn.
Rest and slice: Transfer chicken to a plate and rest 5 minutes. Slice against the grain into strips.
Plate for meal prep: Divide chicken and veggies into 4 containers.
Spoon any pan juices on top for extra flavor.
Garnish and finish: Sprinkle with fresh parsley and serve with lemon wedges if you like a bright finish.