Combine flour, salt, and pepper with a fork in a bowl. Beat egg in a second bowl. Place panko in a third bowl.
Dust chicken tenders with flour mixture to coat. Drench in egg, then in panko until completely coated.
Bring oil up to sizzling in a large frying pan. Add tenders and fry until golden brown on the outside, no longer pink in the center, and the juices run clear, 3 to 5 minutes per side.
Remove tenders to a paper towel-lined plate and sprinkle with Pecorino Romano cheese.
Melt butter in a small saucepan. Add walnuts and saute for 1 minute. Transfer walnut-butter mixture to a food processor; add lemon juice and parsley. Pulse or puree to preferred consistency. Season with salt and pepper. Serve sauce with warm tenders.