12 hours prior to cooking, spatchcock the chicken by using kitchen shears to remove the spine and flip breast-side up. Optionally remove the rib bones and sternum. If not removing, press down with the heel of your palm on the breast bone to flatten. Cover both sides of the chicken generously in diamond crystal kosher salt. Set on a wire rack over a sheet pan and place in the fridge, uncovered, overnight.
Bring the chicken out of the fridge 30 minutes prior to cooking to allow it to get to room temperature. Use kitchen shears to trim any excess skin or fat from the chicken, collecting about 1/4-1/3 cup of fat, and set aside. Do not discard the trimmings.
Pre-heat the oven to 425ºF.
In your smallest pot, add the chicken fat and skin trimmings and set over low heat. The fat will slowly render out and the fat pieces will shrink. Once there are a few tablespoons of fat rendered in the pot, add 8-10 garlic cloves. Supplement with olive oil if needed to ensure the garlic cloves are submerged.
Continue cooking over low heat for 25-30 minutes or until the garlic cloves are a golden brown color and soft all the way through.
Remove the garlic cloves and set the rendered chicken fat to the side. Discard (or snack on) any remaining fat/skin pieces. Use the tines of a fork to mash the garlic cloves into a paste. If the cloves got too crispy while cooking, use a knife and mince it into a paste.
In a bowl, combine the mashed garlic cloves, 1/2 cup parmesan, zest of 1 lemon, juice of 1/2 lemon, and 1 tbsp of the rendered chicken fat. Add a small pinch of salt and a few cracks of black pepper. Stir into a paste. Set aside.
With the spatchcocked chicken skin/breast side up on a wire rack over a sheet pan, brush the rendered chicken fat all over the chicken skin. Season generously with Diamond Crystal kosher salt and black pepper. Roast in the 425ºF oven for 20 minutes or until the skin is crisp.
After 20 minutes, remove the chicken from the oven and lower the oven temperature to 375ºF. Brush or press the garlic/lemon/parm mixture all over the skin of the chicken. Place back into the 375ºF oven for 15 minutes or until the parmesan is golden and the thickest part of the thigh reaches 165ºF.
Rest for 10 minutes, then carve. Garnish with fresh parsley and lemon wedges.