How to Make It
Make the piquillos ketchup In a large saucepan, combine the vinegar with the sugar, a pinch of salt and 4 cups of water. Bring to a boil, then reduce the heat to low, cover and simmer, stirring every 10 minutes, until syrupy, about 1 hour. Transfer the mixture to a blender, add the piquillos and puree until very smooth. Add more water by tablespoons, if needed, to loosen. Transfer to a bowl and stir in the Tabasco. Season with salt and white pepper. Refrigerate.
Make the fried chicken In a large shallow baking dish, combine the soy sauce with the sesame oil, chile oil, ginger and garlic. Add the chicken and turn to coat. Cover and refrigerate overnight.
Drain the chicken. Line a baking sheet with parchment paper. In a large deep skillet, warm the duck fat over moderate heat to 320°. Meanwhile, spread 8 ounces of the cornstarch in another shallow baking dish and season with salt. Coat the chicken thighs and drumsticks in the cornstarch, patting off the excess and transfer to another baking sheet. Working in batches, fry the chicken until cooked through and an instant-read thermometer inserted into the thickest part registers 160°, about 12 minutes. Transfer the chicken to the prepared baking sheet as it’s done and season with salt, pepper and herbes de Provence. Repeat with the chicken breasts and remaining cornstarch, frying the breasts for about 8 minutes. Serve hot with the piquillos ketchup.
Duck fat is available at specialty food shops and dartagnan.com.