Prep: Preheat oven to 350°F (175°C). Grease and flour your cake pans (standard 8-inch or 9-inch pans).
Melt: In a saucepan over medium heat, gently melt the butter and chopped white chocolate until smooth. Set aside to cool slightly.
Cream: In a large bowl, beat the sugar and eggs until the mixture is light and fluffy. Stir in the melted chocolate mixture and vanilla.
Dry Mix: In a separate bowl, whisk together flour, baking powder, baking soda, and salt. Gradually add this to the wet ingredients until just combined.
Cheesecake Center: In a medium bowl, whisk the cream cheese, powdered sugar, sour cream, and milk until completely smooth.
Layer: Pour half of the cake batter into the prepared pans. Carefully spread the cheesecake filling over the batter, then top with the remaining cake batter.
Bake: Bake for 30–35 minutes, or until a toothpick inserted into the cake portion comes out clean.
Cool: Allow the cakes to cool in the pan for 10 minutes before transferring to a wire rack to cool completely.
