1: In a medium bowl, mix together panko and cheese. Set aside.
2: Set aside flour in a small bowl.
3: Set aside egg in a separate small bowl.
4: Take a slice of zucchini and lightly coat in flour. Tap zucchini against the side of the bowl to get off any excess flour.
5: Coat zucchini slice in egg. Shake off any excess egg drippings.
6: Roll zucchini slice into breadcrumb mixture, pressing slightly to get the breadcrumbs to stick to the zucchini. Repeat with remaining zucchini slices.
7: In a small pan or skillet, add 1/4 cup oil to cover the surface of the pan in a very thin coat of oil and bring oil to medium heat.
8: Working in small batches, carefully place about 5 slices of zucchini into the hot oil.
9: Cook until the bottom turns a golden brown, then flip over and cook the other side until crispy and golden brown.
10: Remove from oil when done and place onto a paper towel-lined plate to soak up some of the excess oil. Repeat with remaining zucchini slices, adding more oil if needed.
11: Sprinkle zucchini slices with parsley and more parmesan cheese if desired. Serve while warm, with a dipping sauce if you like.