Pound chicken breasts with a meat mallet to 1/4-in. thickness; layer with prosciutto and mozzarella. Roll up chicken from a short side; secure with toothpicks., Place eggs and bread crumbs in separate shallow bowls. Dip chicken in eggs, then roll in crumbs to coat. Cut each chicken breast crosswise into 3 slices; place in a greased 13x9-in. baking dish, cut side down. Refrigerate, covered, overnight., Preheat oven to 350°. Remove chicken from refrigerator; uncover and let stand while oven heats. In a small saucepan, heat butter over medium-high heat. Add shallot and garlic; cook and stir until tender, 1-2 minutes. Add wine. Bring to a boil; cook until liquid is reduced to 1-1/2 cups. Pour over chicken., Bake, uncovered, until a thermometer reads 165°, 30-35 minutes. Discard toothpicks before serving.