Remove the outer translucent, papery sheaths from the garlic heads and separate the cloves. Peel the skin off 4 cloves and put the cloves in a mortar or mini chopper. Set the remaining unpeeled cloves aside for now. Add the peppercorns and cilantro roots to the peeled garlic and grind to a smooth paste. Stir in the salt and mix well.
Rub the paste over the chicken quarters, covering them completely and taking care not to tear the skin or separate the skin from the meat. Put the leg quarters in a gallon-size resealable plastic bag, press the air from the bag, and seal the bag closed. Place the bag in the back of the refrigerator, where it is coldest, for 12 to 24 hours.
Take the chicken out of the refrigerator, wipe off all the tiny bits of aromatic paste with a paper towel, and allow the chicken to come to room temperature. Meanwhile, put the reserved unpeeled garlic cloves in a mortar or mini chopper (I don’t recommend chopping them by hand) and grind until the pulp is in coarse shards the size of a match head. Don’t worry if you can’t break down the skins into pieces that small. Set the garlic aside.
Pour the oil to a depth of 3 inches in a large wok of Dutch oven and heat to 300°F. Line a sheet pan with paper towels and set near the stove. When the oil is hot, working in batches if needed to prevent crowding, gently lower the chicken pieces, flesh side down, into the oil, making sure they are fully submerged. When all of the chicken pieces are in the oil, the temperature will drop slightly; adjust the heat as needed to keep it between 260°F and 280°F. Deep-fry the chicken, undisturbed, until the pieces feel firm and the skin has turned light brown all over and dark brown around the edges, about 10 minutes. Turn the heat to the highest setting, turn the chicken, skin side down, and keep frying until the skin on each piece is golden brown and small cracks are visible at the “ankles” of the chicken, about 10 minutes. Transfer the chicken pieces, skin side up, to the prepared pan and leave to cool. If frying in batches, lower the heat to bring the oil temperature back down to 300°F and repeat the process.
After the last batch of chicken has been removed from the oil, keeping the heat at the highest setting, sprinkle the pounded garlic evenly over the surface of the hot oil. Be careful, as the oil will foam up 2 to 3 inches high. Once that happens, stir down the oil promptly and swiftly with a mesh skimmer to prevent an overflow. Deep-fry the garlic, stirring constantly, until it turns the color of honey and is thoroughly crisp, less than 20 seconds. Turn off the heat and scoop every bit of the garlic out of the oil onto the prepared pan. You will need to work quickly before the residual heat burns the garlic and turns it bitter.
You can leave the leg quarter whole or separate the thighs from the drumsticks at the joint. If you’d like to serve the chicken the way they do it at Polo, separate the thighs from the drumsticks at the joint and cut each thigh and each drumstick in half across the bones. (In order to avoid crushing the bones and creating dangerous shards, you need to use a large, sturdy cleaver and swift, decisive blows. Do it unthinkingly, unblinkingly like a robot.) By cutting the pieces crosswise, the muscles are shortened, which makes the meat easier to eat.
Arrange the slightly-warmer-than-room-temperature chicken on a platter, sprinkle the crispy garlic all over the top, and serve immediately with the rice and sweet chile sauce.