Preheat oven to 375°F. Line a rimmed baking sheet with foil. Place each chicken breast half between two sheets of plastic wrap. With a rolling pin, pound chicken to an even 1/2-inch thickness. Mix flour, thyme, cayenne pepper, salt and pepper. In a second shallow dish, whisk eggs to combine. Spread cornflake crumbs on a second rimmed baking sheet.
Dip chicken into seasoned flour, turning to coat, then dip in egg mixture. Remove chicken, allow excess egg to drip off, then press both sides into cornflakes. Transfer to baking sheet. Discard remaining flour, egg and cornflakes.
Drizzle chicken with melted butter. Bake until coating is crisp and chicken is cooked through, about 30 minutes.