Preheat oven to 425°F (220°C). Line a large rimmed baking sheet with parchment paper if desired.
In a large bowl, whisk together balsamic vinegar, olive oil, soy sauce, lemon juice, minced garlic, honey, rosemary, paprika, salt, and pepper.
Pat chicken thighs completely dry with paper towels and add them to the bowl with the balsamic mixture. Toss to coat evenly and set aside to marinate while you prep the vegetables.
In another bowl, toss prepared vegetables with olive oil, minced garlic, salt, pepper, and rosemary until evenly coated.
Evenly spread vegetables on a sheet pan, then arrange chicken thighs skin-side up on top of the vegetables.
Roast for 40-45 minutes, or until chicken reaches 165°F internally and vegetables are tender and caramelized. Halfway through cooking, remove the pan from the oven and flip vegetables.
Optional: Broil for 2-3 minutes at the end for extra crispy skin. Drizzle with more balsamic glaze for serving.