Pound the chicken breasts to about ¼ inch thickness. Coat lightly with salt and pepper.
In a small bowl mix together the flour, ½ t. salt and ¼ t. of pepper.
In another small bowl beat the egg with ½ T. of water.
Pour the breadcrumbs into a 3rd small bowl.
Dip the chicken into the flour and coat, dip into the egg mixture, then coat with the breadcrumbs.
Heat the 1 T. olive oil in a pan over medium heat and cook the chicken until golden brown, about 2 minutes per side. Place the chicken breasts on a sheet pan in the oven for about 10 minutes to continue to warm/cook while preparing the sauce.
Wipe the pan clean, then melt the butter. Add in the wine, lemon juice, lemon halves, ½ t. of salt and ¼ t. of pepper. Bring this to a boil, then lower to a simmer for about 2 minutes, until the sauce is thick and reduced to about half. Add in the last 2 T. of butter and mix until it's melted and blended in. Discard the lemon halves.
Remove the chicken from the oven pans, drizzle with the sauce and sprinkle with the parsley and serve. Garnish with additional lemon slices if desired.