Preheat oven to 350 degrees F. Unwrap peppermint kisses and set aside.
In a large food processor or blender, crush the Oreo cookies into fine crumbs Add the melted butter to the crushed Oreos and press into the bottom and up the sides of a 9-inch round springform pan using a measuring cup with a flat bottom. Bake for 5-7 minutes, then remove from oven to cool while preparing the filling.
Beat cream cheese, sugar, and vanilla in a large bowl until smooth. Add the eggs, mixing on a medium-low speed until combined. Set aside 1 cup of batter, then spread remaining batter in the prepared crust.
Place 30 of the peppermint kisses in a medium microwave-safe bowl along with the milk and heat at MEDIUM (50%) power for 60-90 seconds, stirring every 20 seconds until melted.
Stir the melted kisses into the reserved cheesecake batter along with 1 to 2 drops of red food coloring (if using) for a more intensely pink color. Drop spoonfuls of the pink peppermint filling onto the cheesecake. Gently swirl with a knife for a marbled effect.
Bake for 45 to 50 minutes, just until center is almost set but still slightly jiggly. Turn oven off and crack the oven door to allow the cheesecake to cool slowly for the first 20-30 minutes. Remove from oven and loosen the sides of the cheesecake from the pan using a sharp knife. Cool completely at room temperature, then chill before removing the sides of the springform pan.
Chop most of the remaining candy cane kisses (you might want to reserve some whole for decorating the top if not using peppermint bark squares). Sprinkle the chopped kisses over the cooled cheesecake.
Combine the heavy cream, powdered sugar, and vanilla in a bowl and beat with an electric mixer until stiff peaks form. Transfer to a piping bag fitted with a decorative tip and use to pipe swirls around the top of the cheesecake. Stick squares of peppermint bark between the whipped cream swirls before serving.