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Step 1
Spatchcock the chicken: Place the chicken breast-side down. Starting at the neck, use poultry shears to cut along both sides of the spine to remove the backbone. Switch to a sharp knife and cut out the rib cage. (Reserve the backbone and rib cage for another use, such as stock.) Flip the chicken over so it’s breast-side up, and press down on the breastbone to crack it slightly. To remove the thigh bone, cut the ball joints on each end of the bone to pop them out, then cut along both sides of the bone until it is loose enough to remove. (Removing the thigh bones helps the bird lie flatter in the pan during cooking.)
Step 2
To a blender or food processor, add the feta and 2 cups of water and blend until smooth. Transfer to a large bowl and stir in 2 additional cups of water.
Step 3
In a 9- by 13-inch glass baking dish, place the chicken skin-side down. Cover with a layer of cheesecloth, then add the peppercorns, oregano, garlic, bay leaf, and lemon on top. Pour the feta brine over the cheesecloth and seasonings so the chicken is nearly submerged. Cover the dish with plastic wrap and refrigerate for at least 8 hours, or up to 24.
Step 4
Position a rack in the lower third of the oven and preheat to 425°F.
Step 5
Retrieve the chicken from the fridge and discard the cheesecloth, brine, and seasonings. On a large baking sheet, place the chicken breast-side up and pat thoroughly dry with paper towels. Tuck the wing tips behind the shoulders and set aside to air-dry for 30–40 minutes.
Step 6
To a large cast iron or oven-safe skillet over medium-high heat, add the vegetable oil. When it’s hot and shimmering, add the chicken skin-side down, ensuring the skin on the legs is in contact with the skillet. Cook until the skin begins to turn golden brown, 4–6 minutes. Put a smaller cast iron or oven-safe skillet on top of the chicken to weigh it down. Carefully transfer the weighted skillet to the oven and bake until an instant-read thermometer inserted into the thickest part of the thigh reads 170°F and the skin is deep golden brown, about 35 minutes.
Step 7
Remove from the oven, remove the weight from the top of the chicken, and use tongs or a large spatula to gently flip the chicken, ensuring the skin hasn’t stuck to the skillet. If the skin begins to tear while flipping, allow the chicken to sit, skin-side down, until it easily releases from the skillet, 1–2 minutes. Transfer the chicken to a cutting board and set aside to rest skin-side up for at least 5 minutes.
Step 8
Meanwhile, make the herb sauce: in a small bowl, combine the olive oil, chile, mint, parsley, scallions, paprika, and oregano. Zest the lemon directly into the bowl and stir to combine, then cut the zested lemon into wedges to serve with the chicken.
Step 9
To serve the chicken, cut off the legs, then separate the drumsticks from the thighs. Cut each thigh in half. Cut the breasts off the bone and slice each one into thirds, then cut the wings off. (You will have 2 drumsticks, 4 thigh pieces, 6 breast pieces, and 2 wings.) Arrange the chicken pieces on a platter, spoon the herb sauce on top (or serve on the side), and scatter the feta and additional mint leaves around the platter. Serve with the lemon wedges.