Preheat the oven to 425°F (220°C).
In a small bowl, whisk together the sweet paprika, minced thyme, and salt and pepper to taste (about 1 teaspoon salt and 1/2 teaspoon pepper recommended).
Place the potatoes, cherry tomatoes, sliced poblano, bell pepper, and sliced garlic in a large bowl. Drizzle with 1 tablespoon of the olive oil and toss to coat the vegetables evenly.
Transfer the vegetables to a rimmed baking sheet and arrange the potato wedges cut-side down. Sprinkle about 2 teaspoons of the paprika‑thyme seasoning over the vegetables.
In the same large bowl, add the chicken thighs. Drizzle with the remaining 2 tablespoons of olive oil and toss to coat. Sprinkle the remaining seasoning over the chicken.
Place the seasoned chicken thighs on top of the vegetables on the baking sheet, skin side up.
Roast in the preheated oven until the chicken is golden and crisp and an instant‑read thermometer inserted into the thickest part of a thigh reads 180°F (about 45–50 minutes).
Remove from the oven and let rest for 5 minutes, then garnish with minced parsley and serve.