Preheat the oven to 400 degrees F (200 degrees C).
Sprinkle chicken breasts with salt and pepper. Coat chicken breasts in sour cream then coat with pesto.
Stir panko, Parmesan cheese, and Cantanzaro herbs together in a shallow dish; season with black pepper. Press each chicken breast into panko mixture.
Heat an oven-safe skillet on medium-high heat; add oil and butter. Once mixture is shimmering, carefully add chicken breasts. Allow to fry for 3 to 4 minutes on each side.
Place skillet in the preheated oven, and bake chicken until no longer pink at the center, about 12 minutes. An instant-read thermometer inserted near the center should read 165 degrees F (74 degrees C).
