Cut each breast in half and pound to about 1/2" thick.
Beat egg and water in a shallow bowl until blended.
Add garlic, salt and pepper and whisk to blend.
Place parmesan in another shallow bowl.
Dip each piece of chicken in egg mixture making sure to coat.
Allow excess egg to drip off.
Place in parmesan. Sprinkle more parmesan over top. Gently press, then turn and repeat on other side. Shake off excess. Repeat with remaining chicken.
Place butter and oil in a large skillet over high heat.
Place chicken and do not move until edges brown (so that cheese sticks to chicken, about 3 minutes).
Lightly press with spatula then turn over and again do not move until browned.
Lightly press with spatula and remove to serving plate.