For the stuffed chicken: Preheat oven to 350 degrees F.
Carefully slice a slit along edge of the thickest part of each chicken breast to create a pocket. Stuff a slice of prosciutto and 1-ounce mozzarella into each, secure with toothpicks as needed, and place on a baking sheet. Season with salt and pepper and brush with olive oil. Place in the oven and roast until fork tender about 45 to 50 minutes.
For the Orange Beurre Blanc:
Combine the orange juice and wine in a saucepan and simmering on medium heat until reduced by half the volume. Stir in heavy cream, bring to a gentle simmer, and allow to reduce and thicken over low heat. Stir in parsley and set aside briefly in a warm place.
Remove any toothpicks from chicken and place on serving dish. Whisk butter into sauce just before serving, and drizzle sauce around and over the chicken.