Hanukkah Chicken

3 lb. skinless, boneless chicken thighs
1/4 tsp. cayenne pepper
Kosher salt, freshly ground pepper
2 lb. russet potatoes, peeled, coarsely shredded on the large holes of a box grater or in a food processor
1 small onion, peeled, shredded on the large holes of a box grater or in a food processor
2 Tbsp. matzo meal
1 large egg
1/2 cup plus 2 Tbsp. vegetable, canola, or grapeseed oil, divided
3 Pink Lady apples (about 1 1/2 lb.), sliced into 1/2" wedges
1/2 cup dry white wine
1 1/2 cups unsweetened applesauce
4 sprigs thyme
2 Tbsp. fresh lemon juice
1/4 cup coarsely chopped parsley leaves
2 tsp. finely grated lemon zest

Place a rack in oven as close to broiler as possible; preheat broiler. Season chicken on all sides with cayenne, 1 Tbsp. salt, and 1 tsp. black pepper. Let sit 10–15 minutes.
Meanwhile, working in batches, wring out excess moisture from shredded potatoes and onion in a clean dish towel over the sink (the more liquid you remove, the crispier your latkes will be, so take your time and use several towels if necessary). Transfer potatoes and onion to a large bowl.
Whisk matzo meal, 2 tsp. salt, and 1 tsp. pepper in a medium bowl. Add egg and whisk to combine. Add to potato mixture and mix to evenly distribute.
Heat 1/4 cup oil in a 10" ovenproof (preferably cast-iron) skillet over medium-high until shimmering. Carefully transfer potato mixture into hot oil in skillet and use a rubber spatula to spread it into an even layer, pressing to flatten as much as possible. Cook until edges are just starting to brown, about 5 minutes. Brush 2 Tbsp. oil over and transfer skillet to broiler. Broil, checking often to make sure latke isn’t burning, until top is crisped and deeply golden brown, 10–12 minutes.
While latke is in the oven, heat remaining 2 Tbsp. oil in a large skillet over high. Working in 2 batches, cook chicken flat side down until golden brown, about 4 minutes. Turn and cook until other side is golden brown, about 1 minute. Transfer to a plate.
Cook apples in hot oil and fat in pan over medium-high heat, stirring occasionally, until caramelized and softened, 8–10 minutes. Add wine and cook, stirring occasionally, until reduced by half, 2–3 minutes. Using a slotted spoon, transfer apples to a medium bowl, leaving reduced wine behind in skillet. Add applesauce, thyme, and 3/4 tsp. salt to skillet and stir to combine. Nestle chicken into sauce in skillet. Pile apple mixture over chicken. Cover and cook over medium heat until chicken is cooked through, about 15 minutes.
Carefully invert skillet with latke onto a cutting board, then slice latke into 8 wedges.
Drizzle lemon juice over chicken. Toss parsley, lemon zest, and 1/4 tsp. salt in a small bowl. Sprinkle over chicken and apples. Serve chicken with latke wedges alongside.