Heat oven to 375°F. Meanwhile, use a sharp knife to cut a slit in the side of each chicken breast forming a pocket (or have the meat retailer do this for you).
Combine pepperoni, basil and cheese; stuff into pockets. Pinch edges together to close.
Place chicken on a rimmed baking sheet. Spread mustard over chicken. Toss together breadcrumbs and oil; sprinkle over chicken.
Bake 25 minutes or until chicken is cooked through.
For an optional dipping sauce to serve alongside the chicken breasts combine 2 tablespoons Dijon mustard with 1 tablespoon dry sherry.