Place the chicken breasts on a cutting board and slice each diagonally into four or five strips.
Mix the flour, salt, and pepper on a plate.
Beat the eggs with a tablespoon of water on a separate plate.
Combine the breadcrumbs and Parmesan on yet another plate.
Dip the chicken breasts on both sides in the flour mixture, then dip both sides into the egg mixture and roll in the bread-crumb mixture, pressing lightly to coat.
Heat one tablespoon of butter and one tablespoon of olive oil in a large saute pan and cook the chicken strips on medium-low heat for approximately three minutes on each side, until just cooked through.
Add more butter and oil and cook the rest of the chicken breasts.