Preheat oven to 400 degrees Fahrenheit and line a large roasting pan with parchment paper or aluminum foil. Toss potato wedges and baby carrots together in the pan with olive oil, half of the salt, and half of the black pepper. Spread them out in a single layer for even roasting and caramelization.

Pat chicken leg quarters dry with paper towels. Combine melted butter with minced garlic, rosemary, thyme, paprika, and remaining salt and pepper in a small bowl. Brush herb mixture generously all over the chicken, getting under the skin if possible.

Place seasoned chicken skin-side up on top of the potatoes and carrots, nestling them so pan juices drip down and flavor the vegetables. Roast for 30 to 35 minutes until chicken skin is golden brown and crispy and internal temperature reaches 165 degrees Fahrenheit at the thickest part of the thigh.

During the last 5 minutes of cooking, scatter green peas over the vegetables to warm through. Remove from oven and garnish with fresh rosemary sprigs and extra black pepper if desired.