Pound chicken to 1/4-inch thickness (thinner around edges; season with salt & pepper.
Cut frozen compound butter into four strips, about 1-inch x 2-inches. Store remaining butter in freezer.
Place butter on each chicken piece, fold in edges and roll chicken tightly around butter, completely encasing. Repeat with remaining chicken. Freeze for 1 hour.
Set up breading station with flour (seasoned with salt & pepper) in one dish, beaten eggs in a second dish, and panko/parmesan/parsley in a third dish. Dip each chicken roll into flour, egg, then panko mixture and repeat. Be sure to press breadcrumbs. Continue with all chicken rolls then freeze for one hour.
Preheat oven to 375 degrees.
Heat 2-inches of canola oil in a Dutch oven over medium-high heat. Brown chicken rolls for 1-2 minutes per side or until deep golden brown. Remove to drain on paper towels. Place browned chicken rolls into a baking dish. Bake for 20 minutes. Let stand for 5-minutes before serving.
Serve on a bed of mashed potatoes. Garnish with parsley.