How to Make It
Preheat the oven to 325°. Pat the chicken dry with paper towels and place breast side up in a 9-by-13-inch baking dish. Starting at the top of the breast, gently separate the skin from the breast and thighs. Season the chicken cavity with salt and pepper and tuck 8 of the thyme sprigs and 4 stalks of the green garlic inside. Rub half of the butter under the skin of the breasts and thighs and rub the remaining butter all over the outside of the chicken; season with salt and pepper. Tie the legs together with kitchen string and drizzle the chicken with the olive oil and lemon juice.
Scatter the lemon quarters, garlic cloves, shallot and the remaining 6 thyme sprigs and 2 stalks of green garlic around the chicken. Roast for about 1 1/2 hours, basting occasionally, until an instant-read thermometer inserted in an inner thigh registers 165°. Transfer the chicken to a carving board and let rest for 10 minutes.
Carve the chicken and transfer to a platter along with the green garlic, lemon wedges and garlic cloves. Spoon the pan sauce over the top and serve.