Preheat the oven to 350°F (175°C). Grease the bottom of a 9-inch springform pan and line it with parchment paper.
In a mixing bowl, combine the flour, sugar, baking soda, cocoa powder, and salt for the red velvet layer. Mix well.
In another bowl, whisk together the vegetable oil, egg, buttermilk, red food coloring, vanilla extract, and vinegar until smooth.
Gradually add the wet ingredients to the dry ingredients and mix until just combined.
Pour the red velvet batter into the prepared springform pan, spreading it evenly. Bake for 25-30 minutes or until a toothpick comes out clean. Remove from oven and let it cool completely.
While the red velvet layer is cooling, prepare the cheesecake layer. In a mixing bowl, beat the softened cream cheese and sugar with an electric mixer until smooth and creamy.
Add the vanilla extract and beat in the eggs one at a time until well incorporated. Finally, mix in the sour cream until smooth.
Pour the cheesecake mixture over the cooled red velvet layer in the springform pan. Bake for an additional 45-50 minutes, or until the center is set but still slightly jiggly.
Allow the cheesecake to cool at room temperature for 1 hour, then refrigerate for at least 4 hours, preferably overnight.
Before serving, top the cheesecake with sliced strawberries. Optionally, dust with powdered sugar for extra sweetness.