Preheat oven to 400°F.
In a large measuring cup or in a small bowl, whisk together the melted butter, garlic, brown sugar, thyme, basil, oregano, rosemary, salt, pepper, and cayenne.
Arrange the potatoes, Brussels sprouts, carrots, and onion in a single layer on an extra large rimmed baking sheet (about 15 x 20 inches). Drizzle about 3 tablespoons of the butter mixture over the veggies; toss to coat.
Nestle the chicken thighs (skin side up) among the vegetables. Brush the remaining butter mixture over the chicken thighs. The smashed garlic cloves can roast on the pan along with the chicken and veggies.
Roast in the oven for about 35-40 minutes, or until the chicken reaches an internal temperature of 165°F and the vegetables are tender. Stir the vegetables halfway through for even browning. Place the tray under the broiler for 1-2 minutes at the very end to get the skin nicely browned and crispy. Just keep a close eye on it, since the chicken and veggies can burn quickly under the broiler.