Set up a station to bread the chicken. One dish with flour and ½ tsp salt, one dish with egg beaten with water, and one dish with breadcrumbs, lemon zest, 1 tsp salt, black pepper, fresh parsley, and Parmesan cheese.
Dredge the chicken breast in flour, dip in eggs and coat in the panko making sure to press the breadcrumbs into the chicken. Repeat with remaining chicken breasts.
Heat oil in a large rimmed skillet over medium-high heat (you do not want the oil too hot or it will burn the coating). The oil should register at 350°F when temped with an instant read thermometer.
Once oil is hot place chicken gently in the skillet. Cook until golden brown and a thermometer inserted into chicken reads 165°, about 4-5 minutes on each side. Drain on paper towel lined plates. The chicken should be golden brown and breading firm and crunchy. Make the Hollandaise while the chicken rests.