On a large plate, mix the flour with the Parmesan, parsley, garlic, salt and pepper. In a shallow bowl, beat the eggs to mix. Gently pound the pieces of turkey 1/3 inch thick. Dip the turkey pieces in the egg, then roll in the flour mixture, patting off the excess.
In a large skillet, melt 1 tablespoon of the butter in 1 tablespoon of the olive oil. Add 2 of the turkey pieces and cook over moderately high heat until browned and just cooked, about 3 minutes per side; reduce the heat to moderate when the skillet gets too hot. Transfer the turkey to dinner plates. Repeat with the remaining 1 tablespoon of butter, 1 tablespoon of olive oil and 2 pieces of turkey. Serve with the lemon quarters.