Prepare the Red Velvet Cake Base:

1. Preheat the Oven: Set to 350°F (175°C). Grease and line a springform pan with parchment paper.
2. Mix the Dry Ingredients: In a medium bowl, whisk together flour, sugar, baking powder, baking soda, salt, and cocoa powder.
3. Mix the Wet Ingredients: In another bowl, combine vegetable oil, buttermilk, eggs, vanilla extract, vinegar, and red food coloring until smooth.
4. Combine the Batter: Gradually add the dry ingredients to the wet ingredients, stirring until just combined. Do not overmix.
5. Bake: Pour the batter into the prepared springform pan and bake for 25-30 minutes or until a toothpick inserted in the center comes out clean.
6. Cool the Cake: Let the cake cool completely in the pan before adding the cheesecake layer.

Prepare the Strawberry Cheesecake Filling:

1. Beat the Cream Cheese: In a large mixing bowl, beat cream cheese until smooth.
2. Add Sweetness: Mix in powdered sugar and vanilla extract until well combined.
3. Incorporate Strawberries: Stir in the pureed strawberries for a fruity flavor.
4. Fold in Whipped Cream: In a separate bowl, whip heavy cream until stiff peaks form, then gently fold it into the cheesecake mixture.

Assemble the Cake:

1. Layer the Cheesecake: Once the red velvet cake base is completely cool, spread the strawberry cheesecake filling evenly on top.
2. Chill: Refrigerate for at least 4 hours (or overnight) to allow the cheesecake to set.
3. Decorate: Before serving, top with fresh halved strawberries and whipped cream if desired.