Prepare the chicken: Season the flesh side of the chicken with half of the salt, the paprika, lemon zest, and olive oil. Flip and season the skin side with the remaining salt. Place in the refrigerator skin-side up, uncovered, and let rest for 24 hours.
2. Make the aioli: In a medium bowl, whisk together the salt, egg yolks, and lemon juice. While whisking constantly, slowly drizzle in the oil until emulsified. Season to taste with salt.
3. Make the paste: Smash all the ingredients together in a mortar and pestle until the coriander seeds have popped. Set aside.
4. Cook the chicken: Heat the canola oil in a large cast-iron skillet over medium-high. Add the chicken, skin-side down (make sure the skin is stretched over the chicken to avoid any exposed skin!), and reduce the heat to medium. Wrap a slightly smaller cast-iron pan in foil and press on top of the flesh-side of the chicken. Cook until the skin is crisp and the chicken is almost nearly cooked through, 15 to 20 minutes. Remove the cast-iron skillet and carefully drain off the fat. Flip the chicken over in the skillet. Remove from the heat and let the chicken rest and carry over cooking in the skillet for around 10 more minutes.
5. Meanwhile, Make the sauce: Heat olive oil in a large saucepan over medium-high. Add the garlic and cook until just toasted, about 30 seconds to 1 minute, then immediately add the onions to stop the garlic from cooking any more. Cook until the onions are soft, 3 minutes, then stir in the prepared chili paste. Cook until fragrant, about 30 seconds, then add the wine. Cook until reduced by half, then stir in the chicken stock, bay leaves, and lemon peel. Bring to a simmer and reduce by half, 25 to 30 minutes. Season to taste with the sherry and salt. Keep warm.
6. To serve, transfer the chicken to a serving platter with a ramekin of the aioli. Drizzle the pan drippings over the chicken and top with some of the piri piri sauce. Drizzle with some olive oil and serve with fries.
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