Preheat oven to 400°F (200°C). Brush an oven-safe skillet with vegetable oil.
In a bowl, mix cherries, bread crumbs, egg yolk, olive oil, garlic, cheese, herbs, salt, pepper, and cayenne.
Cut a slit in each chicken breast and pound to ½-inch thickness.
Divide stuffing between breasts, roll tightly, and wrap in plastic to shape.
Overlap 2 prosciutto slices; unwrap chicken and roll prosciutto tightly around it. Repeat with second breast.
Tie each roll with kitchen twine to secure.
Place chicken in skillet and bake 25 minutes, until prosciutto is browned and chicken reaches 165°F.
Remove chicken and tent with foil.
Add broth and balsamic vinegar to skillet; boil and reduce by half, scraping browned bits.
Stir in butter until glossy.
Remove twine, slice chicken, and drizzle with sauce to serve.