Prep the Dish: Preheat oven to 400°F. Spread the sliced shallots evenly across the bottom of a large casserole dish or roasting pan. Scatter about half of the garlic cloves over the shallots, then add the thyme and rosemary on top.
Season the Chicken: Pat the chicken leg quarters dry with paper towels. Drizzle both sides with the oil and season generously with salt and black pepper. Place the chicken skin-side up over the shallots and garlic.
Add Remaining Garlic: Tuck the rest of the garlic cloves around and between the chicken pieces.
Add Wine & Broth: Pour the chicken broth and white wine around the edges of the pan (avoid pouring directly on the chicken so you don’t wash away the seasoning).
Roast: Roast uncovered for 55–65 minutes, or until the chicken skin is golden and crispy and the internal temperature reaches 165°F. For extra-crispy skin, broil the top for the last 5–7 minutes.
Baste: Remove from the oven and spoon the pan juices over the chicken to keep the skin glossy and the meat juicy.
Serve: Serve warm over mashed potatoes with plenty of the pan sauce, roasted garlic, and shallots.