Preheat oven to 325°F (163°C). Line the bottom of a springform pan with parchment paper and lightly grease the sides.
In a bowl, whisk together flour, cocoa powder, baking soda, and salt. In another bowl, combine buttermilk, vinegar, vanilla, and red food coloring.
In a large mixing bowl, beat sugar and oil until combined. Add the egg and mix well. Alternate adding dry and wet ingredients, mixing until smooth. Pour batter into the prepared pan.
Bake red velvet cake for 20–25 minutes. Let it cool slightly while preparing the cheesecake layer.
In a clean bowl, beat cream cheese and sugar until smooth. Add sour cream, vanilla, and eggs one at a time, mixing well after each. Fold in strawberry purée.
Pour cheesecake mixture over the cooled cake layer. Bake for 50–60 minutes or until the center is set but slightly jiggly.
Turn off the oven, crack the door, and let the cheesecake cool inside for 1 hour.
Refrigerate for at least 4 hours, preferably overnight.
Before serving, top with whipped cream, strawberries, and white chocolate shavings if desired.