Brine the Chicken: Combine all Brine ingredients in a bowl. Add chicken breasts and brine for 2-4 hours.
Prepare the Egg Wash: Whisk together eggs, heavy cream, and Dijon mustard from the Egg Wash group.
Prepare the Parmesan Crust: Combine Parmigiano-Reggiano cheese, Panko bread crumbs, almond flour, Garlic powder, and Dried thyme from the Parmesan Crust group in a shallow dish.
Coat the Chicken: Remove chicken from brine, pat dry, and dredge in the Egg Wash, then dredge in the Parmesan Crust, pressing to adhere.
Bake the Chicken: Place coated chicken breasts on a baking sheet and bake at 400°F (200°C) for 20-25 minutes, or until cooked through and golden brown.
Prepare the Lemon-Caper Butter Sauce: While chicken is baking, melt 2 tbsp of butter in a saucepan over medium heat. Add Garlic and cook for 1 minute until fragrant.
Deglaze and Reduce: Deglaze the pan with white wine and cook until almost evaporated. Add Chicken stock and simmer until reduced by half.
Emulsify the Sauce: Whisk in remaining cold butter, one cube at a time, until emulsified and smooth. Stir in Lemon juice, Capers, Parsley, and Red pepper flakes.
Serve: Drizzle Lemon-Caper Butter Sauce over baked chicken breasts and serve immediately.