1. Preheat oven to 350 degrees F.
2. In a large bowl, beat the cream cheese and sugar until light and fluffy. Add the eggs and beat well. Add the sour cream and vanilla; mix well.
3. Place 1/2 cup of the cream cheese mixture in a small bowl and stir in the peppermint extract and red food color; mix well. Pour remaining cream cheese mixture into the pie crust.
4. Drop the peppermint mixture by spoonfuls into the mixture in the crust and swirl with a knife to create a marbled effect.
5. Bake cheesecake for 30-35 minutes or until edges are set (the center will be slightly loose). Allow the cake to cool for 1 hour, then cover it and chill for at least 6 hours before serving.
6. To make it holiday-festive, garnish each slice of cheesecake with a dollop of whipped cream and a miniature candy cane.