Preheat your oven to 400 degrees F. Position the rack in the center of the oven. High heat is what gives you crispy chicken skin and caramelized vegetables, so do not drop the temperature.

Add the carrots, parsnips, potatoes, onion wedges, and smashed garlic cloves to your sheet pan. Drizzle with 2 tablespoons of the olive oil and season with 3/4 teaspoon of the salt, half the pepper, and the fresh rosemary. Toss everything well with your hands so each piece is coated, then spread the vegetables into a single layer. Try to cover most of the pan surface. The vegetables should be touching the pan, not piled on top of each other.

Pat the chicken leg quarters very dry with paper towels. Dry skin is the key to crispiness. Rub each piece all over with the remaining 1 tablespoon of olive oil. Season with the remaining 3/4 teaspoon of salt, the remaining pepper, garlic powder, and smoked paprika, pressing the seasoning into the skin with your hands.

Nestle the seasoned chicken leg quarters directly on top of the vegetables, skin side up. Try to tuck the vegetables under and around the chicken pieces so they sit in the drippings as the chicken roasts. This is what gives the vegetables that slow-cooked, savory flavor.

Roast uncovered for 45 to 50 minutes. Do not open the oven during the first 30 minutes. At the 45-minute mark, check the chicken by inserting an instant-read thermometer into the thickest part of the thigh without touching bone. It should read 165 degrees F. The skin should be deep golden brown and the vegetables should be fork-tender with some caramelized edges.

If the skin needs more color at 45 minutes but the temperature is already at 165 degrees F, switch the oven to broil for 3 to 4 minutes and watch it carefully so it does not burn.

Let the pan rest for 5 minutes before serving. This lets the juices settle back into the chicken so they do not all run out when you cut into it. Serve the chicken directly over the vegetables and spoon any pan drippings over the top.