Preheat the oven to 425°F (220°C).
In a small bowl, combine kosher salt, black pepper, garlic powder, smoked paprika, and dried thyme.
Pat the chicken thighs dry with paper towels. Rub each chicken thigh with olive oil, then evenly sprinkle the spice mixture over all sides of the chicken.
In a large baking dish or rimmed sheet pan, arrange the carrots, baby potatoes, red onion wedges, and whole garlic cloves in a single layer.
Drizzle 1 tablespoon of olive oil over the vegetables and toss gently to coat. Season the vegetables with a pinch of salt and pepper.
Place the seasoned chicken thighs skin-side up on top of the vegetables.
Bake in the preheated oven for 35 to 40 minutes, or until the chicken thighs reach an internal temperature of 165°F (74°C) and the skin is crispy and golden brown.
If desired, broil for an additional 2-3 minutes to crisp the skin further, watching carefully to avoid burning.
Remove the baking dish from the oven and let the chicken rest for 5 minutes.
Garnish with chopped fresh parsley before serving.