In a shallow bowl, mix the grated Parmesan, breadcrumbs and chopped parsley until combined.
In a second shallow bowl, whisk together the flour, cayenne pepper, salt and black pepper.
Beat the eggs in a third shallow bowl until smooth.
Pour vegetable oil into a 12-inch skillet to about 1/2 inch depth and heat over medium-high until shimmering and hot (about 350°F or a drop of batter sizzles immediately).
Working with one piece at a time, dredge a chicken strip in the egg, then coat with the flour mixture, dip back into the egg, and finally press into the Parmesan-breadcrumb mixture to fully coat.
Carefully add coated strips to the hot oil in a single layer and fry until golden brown and cooked through, about 2–3 minutes per side. Do not overcrowd the pan.
Transfer cooked strips to paper towels to drain and repeat with remaining chicken, refreshing the oil if it becomes too dark between batches.
Serve the hot Parmesan chicken strips with ranch dressing for dipping.
