1. Combine prosciutto, pepper, and sage in small bowl.
2. Heat 2 teaspoons oil in 12-inch skillet over medium-high heat. Add shallots, garlic, salt, and rosemary; cook 30 seconds. Add mushrooms; cover and cook 3 to 4 minutes, until mushrooms are softened. Uncover; cook 7 to 8 minutes more until liquid evaporates and mushrooms are browned. Transfer to medium bowl.
3. Meanwhile, with sharp knife, make a 3- to 4-inch slit lengthwise along one side of each breast, cutting almost (but not) through to form a pocket. Stuff each pocket with 1 slice mozzarella. Divide prosciutto mixture and stuff evenly on top of cheese. Place flour in a large plate; add chicken, turning to coat both sides.
4. Combine broth and cornstarch in cup. Heat 2 teaspoons oil in skillet. Add chicken and cook 2 minutes until lightly browned. Gently turn chicken; add remaining 2 teaspoons oil and cook 2 minutes more. Add wine; cook 30 seconds. Add broth mixture and mushrooms. Cover; reduce heat to medium-low and simmer 8 to 10 minutes, until chicken is cooked through. Garnish with parsley. Makes 4 servings.