In a medium bowl, stir together peaches, butter, basil, 1/2 teaspoons salt, and 1/2 teaspoons pepper.
Butterfly pork tenderloin, cutting to but not through pork. Open pork, and place between 2 sheets of heavy duty plastic wrap; pound pork to 1/4" thickness. Spoon peach mixture down center of each tenderloin. Fold over to enclose filling, and wrap pork in prosciutto. Sprinkle with remaining 1/2 teaspoons salt and 1/2 teaspoons pepper.
Preheat oven to 400 degrees.
In a large oven-safe skillet, heat olive oil over medium high heat. Add pork, and cook for 3 minutes per side or until prosciutto begins to brown. Place skillet in oven, and bake for 20 minutes or until a meat thermometer inserted in thickest portion registers 145 degrees. Remove pork from skillet, and let stand for 10 minutes before serving.
Add broth to skillet, and cook over medium-high heat, scraping browned bits from bottom of skillet with a wooden spoon. Cook until broth is reduced to 1 cup; whisk in basil and mustard. Serve sauce over pork.