- For the chicken paillard: Place flour, salt and cayenne in a shallow bowl.
- Whisk eggs until frothy and add to a separate shallow bowl.
- Mix together panko, parmesan, and paprika in a third shallow bowl.
- Generously season both sides of chicken with salt and pepper, then dredge in seasoned flour, shaking off any excess. Next, turn to coat with the egg mixture and lift from the bowl, allowing excess to drip off.
- Finally coat the chicken with the panko mixture, pressing to adhere as much as possible.
- Heat 6 tablespoons oil in a large heavy skillet over medium-high heat. Working in 2 batches, cook cutlets, adding remaining 2 tablespoons oil to pan between batches, until golden brown and cooked through, about 3-4 minutes per side. Transfer to a paper towel-lined plate and season with salt to taste.
- For the milk gravy: Heat the oil in a saucepan over medium heat then whisk in the flour. Cook until it's a light blonde color, about 2 minutes, and then whisk in the broth and Lactaid. Bring the gravy to a simmer and cook until thickened, 2 to 3 minutes.
- Add in the Worcestershire sauce, peppercorns, brine, hot sauce and salt to taste and bring back to a simmer. Check for seasoning and set aside until ready to use. Spoon milk gravy over fried chicken paillard just before serving.