Preheat the oven to 425°F (220°C).
In a small bowl, mix together 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 coat with the spice mixture.
In a large baking dish or rimmed sheet pan, arrange the carrots, red onion wedges, and baby potatoes.
Drizzle the minced garlic over the vegetables and toss them with 1 tablespoon of olive oil and a pinch of salt and pepper.
Place the seasoned chicken thighs on top of the vegetables skin side up.
Bake uncovered in the preheated oven for 35 to 40 minutes, or until the chicken reaches an internal temperature of 165°F (74°C) and the skin is crispy.
Remove from the oven and let rest for 5 minutes.
Sprinkle chopped fresh parsley over the chicken and vegetables before serving.