Reduce the oven temperature to 300°F.
In a mixing bowl, beat the cream cheese and sugar until smooth. Scrape the bowl on the sides and bottom 2 or 3 times and then beat any lumps until they dissolve.
Add the peppermint and beat.
Add the eggs and yolks, one at a time, beating just until blended.
Stir in the cream until mixed.
Divide the batter between two bowls, using a measuring cup to evenly divide the batter. Set the bowl with white batter aside.
To the other bowl of batter, add 6-10 drops of red food coloring. Use fewer drops to make a pink batter and more drops to make a red batter. Stir to mix well.
Set the cooled crust in the springform pan in front of you. Measure ½ cup of white batter and pour it into the center of the cooled crust. Measure the batter carefully so that the stripes will be pleasingly proportioned.
Use another measuring cup and pour ½ cup of the pink batter into the center of the crust on top of the white batter.
Measure ½ cup of white batter again and pour it over the pink batter. Continue alternating colors until both of the batters are used, pouring the batter into the center of the pan each time. Do not shake or lift the pan during the layering process.
Fill a large flat pan with hot water and place it in the preheated oven on the lowest rack.
Place the cheesecake on the rack above the hot water. Bake for 1 hour and 20 minutes. If the cheesecake starts browning on top before the cooking time is up, spray a piece of aluminum foil with cooking spray and place it gently on top of the cheesecake.
At the end of the cooking time, remove the cheesecake from the oven. It will jiggle slightly in the middle when you move it. If it seems liquid in the middle, bake it for an additional 10-15 minutes.
Let the cheesecake cool for 2 hours. Then refrigerate it for 6-8 hours.
Decorate the cake with finely crushed peppermint candies and whipped cream if desired. To serve, remove the pan ring and slice.