To spatchcock the chicken, place it breast-side down on a cutting board. Use sturdy kitchen shears to cut along both sides of the backbone and remove it. Set the backbone aside for stock. Turn the chicken so the neck is at the top and the legs are closest to you. If manageable, use a knife to cut out the ribcage. Flip the chicken over, skin-side up, and press down on the breastbone to flatten it.

For the brine, bring the water to a boil in a large pot over high heat. Add the salt, sugar, soy sauce, garlic, and peppercorns. Once boiling, turn off the heat and squeeze the lemon halves into the pot, adding the rinds as well. Remove the pot from the heat, stir in the ice, and let it cool to room temperature. You should have about 6 ½ cups of brine. Place the chicken in a large bowl and pour the brine over it. If there's extra brine, save it for marinating chicken breasts or thighs. Cover the bowl and refrigerate for at least 12 hours, up to 24 hours.

To soak the rice, combine it with enough water to cover by about an inch in a medium bowl. Let it soak for at least 2 hours or overnight.

An hour before cooking, take the chicken out of the brine and pat it dry with paper towels. Leave it at room temperature, skin-side up. Preheat the oven to 325°F thirty minutes before cooking.

For the rice, drain it in a fine-mesh sieve and return it to the bowl, covering it with water. Rinse the rice by swishing your hands through it, then drain again. While the rice is in the sieve, fill a medium pot with water and fit it with a steamer basket or pasta insert. Line the basket with wet cheesecloth. Place the rice in the cheesecloth in an even layer and cover. Bring the pot to a boil, then reduce to a simmer and steam the rice for 12 to 15 minutes until fully cooked but still firm. Transfer the rice to a heatproof bowl and mix in the garlic, nuts, jujubes, ginger, sesame oil, and salt.

In a 12-inch cast iron skillet over medium heat, melt 1 tablespoon of butter. Add the rice and spread it evenly in the skillet, allowing it to brown for about 3 minutes. Place the chicken skin-side up on the rice, tucking the wing tips underneath, and dot the skin with the remaining butter. If the chicken legs extend beyond the pan, place a sheet pan on the lowest oven rack to catch drips. Transfer the skillet to the oven and roast for 30 minutes. Increase the temperature to 400°F and roast for an additional 25 to 30 minutes, or until the skin is golden, the rice is browned and crisp at the edges, and the chicken is cooked through (the thickest part of the breast should reach 165°F).

Remove the skillet from the oven. Using tongs, transfer the chicken to a cutting board, skin-side up, and let it rest for at least 5 minutes.

To serve, cut the legs off the chicken, separating the drumsticks from the thighs. Remove the breasts from the bone and slice each into thirds, then cut off the wings. Arrange the chicken on a platter alongside the rice.