Remove the spine on the chicken, cut through the top of the sternum then flip skin up and use your palms to gently break the sternum then flatten. Salt the skin, point a fan at it, and let the skin dry out. Alternately, you can cover in paper towels and then plastic and do this in the fridge overnight.
Prep the potato and carrots. Season with salt and place on a strainer over a bowl between the fan and the chicken.
After 30mins (or letting the chicken come up closer to room temp if from the fridge), start heating up a cast iron pan over medium heat and an oven at 175C.
Take the butter, add the grated garlic and the spices, and mix together. Use a teaspoon to get half of the butter between under the breast skin, then press lumps on the skin to distribute. Season the meat side, flip back up, pat the skin dry.
Once the pan and oven are both hot, add a thin sheet of oil that covers the entire surface, then set the chicken down on the pan skin side down. Let the contact area get a good brown sear, then set aside the chicken and pour all hot liquids all over the skin while brushing the rest of the butter all over.
Place potatoes and carrots in the pan, season with pepper, and briefly stirfry in the pan. Off the heat, lay down the chicken skin up over the potatoes and carrots.
Place in the oven and roast for 15mins, then lower to 150C and let cook for 45mins. Turn off heat and leave in the oven for 15mins, then serve in the pan.