Place the chicken with the bottom end facing down on a board and slide a knife along one side of the spine. Open up the chicken and spread it out on the board with the breasts facing up. Push down hard with your hand in the middle to break the spine and flatten the chicken.
Heat the oven to 374°F (190 °C). Take a deep baking tray that can fit the chicken snugly. Put it on a moderate stove and pour in the olive oil. Salt on all sides and braise evenly until golden on both sides, about 5-10 min.
Remove the tray from the stove, transfer the chicken to a large plate and pour out the oil from the tray. Return the chicken to the container, pour in the milk (2/3 of the chicken needs to be submerged in milk). Add the rind and juice of 2 lemons, the garlic cloves, black pepper grains, bay leaf and 1/2 the thyme.
Bake in the oven for 1 hour 30 min., while turning the chicken over every 20 min. and basting it with the milk from the tray every time.
In a small pan with a little olive oil, braise the rest of the thyme to make it crunchy.
Upon serving, distribute the chicken into plates. Pour the sauce over the meat and place the crunchy thyme on top.