In a large mixing bowl, whisk together the balsamic vinegar, Worcestershire sauce, soy sauce, honey, red pepper flakes, and olive oil until well combined.
Add the chicken thighs to the bowl with the marinade, ensuring each piece is well coated. Cover and marinate for at least 30 minutes, or up to 2 hours.
Preheat your oven to 425°F (220°C).
Wash and chop the zucchini into spears, cut the carrots into sticks, and clean the mushrooms. Toss the vegetables with olive oil, salt, and pepper in a separate bowl.
On a large baking sheet, arrange the marinated chicken thighs in the center and surround them with the prepared vegetables.
Transfer the baking sheet to the oven and roast for about 35-40 minutes, stirring the vegetables halfway through.
Once cooked, let it rest for a few minutes before serving warm, drizzling any remaining pan juices over the top.
