Lightly pound chicken breasts to flatten somewhat to an even thickness. Dust the chicken in the flour and set aside.
Make the batter by beating eggs briskly, then beating in the lemon juice, parsley, salt, wine, garlic, hot pepper sauce, and Parmesan. Coat a heavy skillet with olive oil and butter and place over medium-high heat. Dip the floured chicken pieces in the batter; coat generously and place in the heated skillet. Cook until golden brown on each side, about 5 to 7 minutes. Remove chicken from the pan and drain off excess fat. Make the wine sauce; melt the butter in the pan, then stir in the wine and lemon juice. Return the chicken pieces to the pan, spooning the wine sauce over all and cook for about 1 minute longer. Serve immediately.