Preheat your oven to 475°F.
In a large bowl, toss together the cubed vegetables, lemon quarters, thyme sprigs, rosemary sprigs, and salt. Drizzle with the melted butter and stir to coat evenly. Spread the mixture across the bottom of a large roasting pan to form a bed that fully covers the pan's base.
In a small bowl, mix together the thyme leaves and salt. Rub this mixture all over the chicken, making sure to coat the inside cavity as well. Carefully loosen the skin over the breasts without tearing it.
In another small bowl, combine the melted butter with the chopped rosemary. Take a portion of this butter and gently spread it beneath the loosened skin on the chicken breasts.
Place the lemon quarters inside the chicken cavity. Set the chicken on top of the vegetable bed in the roasting pan. Brush the exterior of the chicken with the remaining rosemary butter.
Tie the legs together to hold the shape and roast for 20 minutes. After 20 minutes, lower the oven temperature to 400°F. Continue roasting for about 45 minutes, or until the chicken is fully cooked.
Remove the chicken from the oven and transfer it to a cutting board. Cover loosely with foil and let it rest for 15 minutes. Cover the vegetable bed with foil to keep warm.
With the chicken breast-side up, use a sharp carving knife and meat fork to hold it steady. Cut through the leg joints to remove each leg, separating into drumsticks and thighs. Slice through the wing joints to remove the wings. Carve the breast meat by slicing down along the breastbone and cutting into pieces.
Discard the herb sprigs from the vegetable bed, stir the vegetables, and serve them alongside the carved chicken.
Leftovers can be stored in an airtight container in the refrigerator for up to 4 days.