Grab two shallow dishes and one plate. In the first shallow dish, whisk together the egg, 2 tablespoons of white wine, 1 tablespoon of lemon juice, and cayenne pepper. In the second shallow plate, mix the flour, parmesan cheese, and 1 tablespoon of parsley. Pound the chicken breasts until thin and season with salt and pepper.
To bread the chicken, first, dip the seasoned chicken breasts into the egg mixture. Then, put them into the flour mixture to coat. Put all breaded breasts on the plate.
Heat one tablespoon of olive oil and cook the chicken breasts until brown on both sides, about 3 minutes on each side. Transfer to a clean plate and keep warm.
Using a rubber spatula, scrape the bottom of the skillet as much as you can to remove any burnt bits and pieces, add the remaining tablespoon of oil, and saute the minced garlic with the red pepper flakes for about a minute. Add the remaining white wine and lemon juice, and reduce the mixture by a fourth. Reduce heat, add the butter and remaining parsley, and let it melt. Season with salt and pepper. Pour over the chicken and serve.