Heat the oven to 425°F (220°C) and set a rack in the middle.
Pat the chicken thighs dry with paper towels. Dry skin is what turns crisp in the oven.
On a large rimmed sheet pan, toss the carrots, sweet potato, onion, parsnips and garlic with 2 tablespoons of olive oil and 3/4 teaspoon of salt. Spread them in a single layer.
Rub the chicken with the remaining oil, then season with the thyme, paprika, remaining salt and the pepper. Nestle the thighs skin-side up on top of the vegetables, leaving a little space between pieces.
Roast for 35–45 minutes, until the skin is deep golden and an instant-read thermometer in the thickest part of a thigh (not touching bone) reads at least 165°F (74°C). Thighs are most tender at 175–185°F.
Rest for 5 minutes, then stir the vegetables through the pan juices and serve with lemon wedges.