Preheat oven to 325 degrees F. In a heavy small saucepan, heat and stir 8 ounces white chocolate over low heat until melted and smooth. Remove from heat; set aside.
For crust, in a medium bowl, stir together graham crackers and melted butter until combined. Press crumb mixture firmly onto the bottom of a 9-inch springform pan (do not go up the sides of pan.) Bake for 10 minutes. Remove from oven. Cool on a wire rack.
For filling, in a large mixing bowl, beat cream cheese, mascarpone, sugar, and salt with an electric mixer on medium speed until combined. Beat in melted chocolate and peppermint extract until smooth and combined, scraping bowl. Add eggs one at a time, beating on low speed after each addition just until combined. Stir in 3/4 cup candy.
Pour filling into crust-lined pan. Place pan in a shallow baking pan. Bake for 50 to 60 minutes or until a 2-1/2-inch area around the outside edge appears set when gently shaken.
Cool in pan on a wire rack for 15 minutes. Using a sharp small knife, loosen cake from pan; cool for 30 minutes more. Remove sides of pan and cool completely. Cover cheesecake with plastic wrap and chill in the refrigerator overnight.
To serve, cut cheesecake into wedges using a sharp knife dipped in warm water. In a heavy small saucepan, melt 2 ounces white chocolate over low heat. Spoon melted chocolate over cheesecake slices. If desired, sprinkle top with additional candy. To store any remaining cheesecake, cover and chill in refrigerator up to 2 days. Makes 12 servings.