Kyckling i ostpolenta

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1. 1
   Mix 7 Tbsp. Diamond Crystal or ¼ cup plus 1¼ tsp. Morton kosher salt, 2 Tbsp. paprika, 1 Tbsp. smoked paprika, 1 Tbsp. ground coriander, 1 Tbsp. ground cumin, and 1½ tsp. sugar in a small bowl. Place 3 lb. skinless, boneless chicken thighs (about 8), excess fat trimmed, in a medium bowl and sprinkle ⅓ cup spice mixture over, turning chicken so both sides are coated. Cover chicken and chill 30 minutes. Set remaining spice mixture aside at room temperature.
2. 2
   Heat ½ cup vegetable oil, 1 Tbsp. cayenne pepper, 1 Tbsp. paprika, 1 Tbsp. light or dark brown sugar, ½ tsp. chili powder, ½ tsp. garlic powder, and 1 tsp. Diamond Crystal or ½ tsp. Morton kosher salt in a large saucepan over medium heat until oil is slightly bubbling and thermometer registers 130°, about 5 minutes. Let spiced oil cool.
3. 3
   Toss 1 bunch parsley, leaves with tender stems picked, ½ bunch mint, leaves picked, 4 scallions, thinly sliced, 2 garlic cloves, finely grated, and zest and juice of ½ lemon in a small bowl to combine. Drizzle 1 tsp. spiced oil over and season with salt; toss to coat herbs. Set gremolata aside. Set remaining spiced oil aside separately.
4. 4
   Cook 6 oz. guanciale, finely chopped, and 6 oz. pancetta, finely chopped, in a medium Dutch oven or other heavy pot over medium heat, stirring occasionally, until beginning to brown around edges, about 5 minutes. Using a slotted spoon, transfer to a plate.
5. 5
   Cook 10 oz. spicy Italian sausage in same pot, breaking up into small pieces and stirring occasionally with a wooden spoon, until golden, 7–9 minutes. Return guanciale and pancetta to pot and stir to combine. Add ¼ medium white onion, finely chopped, 1 bay leaf, 1½ tsp. five-spice powder, 1 tsp. freshly ground pepper, ¼ tsp. ground allspice, ¼ tsp. ground coriander, and ¼ tsp. ground cumin to pot and mix well. Cook, stirring occasionally, until onion is translucent and spices are fragrant, about 4 minutes. Pour in 4 cups low-sodium beef broth and bring to a simmer, stirring occasionally, 6–8 minutes. Pluck out bay leaf; discard. Reduce heat to low and keep gravy warm until ready to use.
6. 6
   Whisk 1½ cups stone-ground grits and ½ cup fine-ground polenta in a small bowl to combine. Bring 4 cups water to a boil in a large saucepan. Add polenta mixture and return to a simmer, whisking constantly. Whisk in 4 Tbsp. unsalted butter, then add 1¼ cups whole milk, ½ cup coarsely grated cheddar, ½ cup coarsely grated Monterey Jack, and 1 Tbsp. Diamond Crystal or 1¾ tsp. Morton kosher salt and cook, whisking, until cheese is melted and there are no lumps in polenta, 2–3 minutes. Reduce heat to low and keep polenta warm until ready to use.
7. 7
   Whisk 4 large eggs, ⅓ cup buffalo sauce, and ½ cup water in a shallow bowl until eggs are incorporated and foamy. Whisk 2½ cups all-purpose flour, 2 Tbsp. cornstarch, and 3 Tbsp. reserved spice mixture (you will have a little left over) in another shallow bowl to combine.
8. 8
   Pour vegetable oil into a large Dutch oven or other heavy pot fitted with thermometer to come 2" up sides. Heat oil until thermometer registers 350°. Working with 1 piece at a time, dip chicken into egg mixture to coat, letting excess drip back into bowl. Transfer to flour mixture and dredge, shaking off excess. Place on a rimmed baking sheet.
9. 9
   Carefully drop 4 chicken thighs into oil and cook, turning occasionally and adjusting heat as needed to keep oil between 300°–325°, until golden brown and crisp, 8–10 minutes. Using tongs, transfer to a wire rack set inside another rimmed baking sheet; season immediately with salt. Repeat with remaining chicken. Brush reserved spiced oil over chicken.
10. 10
    Spoon polenta onto plates; arrange fried chicken on top. Pour some reserved gravy over, then top with reserved gremolata and torn tender herbs (such as parsley, mint, and/or dill if using).