Step 1: Prepare the Cake Layer

1. Preheat oven to 350°F (175°C) and grease a 9-inch springform pan.
2. In a mixing bowl, beat butter and sugar until light and fluffy. Add eggs and vanilla extract, mixing until combined.
3. Sift together flour, baking powder, and salt. Gradually add to the wet ingredients, alternating with milk.
4. Pour batter into the prepared pan and bake for 25 minutes until golden brown. Let cool completely.

Step 2: Make the Cheesecake Layer

1. In a large bowl, beat cream cheese and sugar until smooth.
2. Add eggs one at a time, mixing at low speed to avoid incorporating too much air.
3. Stir in vanilla extract and sour cream until fully combined.
4. Pour cheesecake batter over the cooled cake layer and smooth the top.

Step 3: Bake the Cheesecake Cake

1. Place the springform pan in a larger baking dish. Fill the dish with hot water halfway up the sides (water bath method).
2. Bake at 325°F (160°C) for 40 minutes, until the edges are set but the center is slightly jiggly.
3. Turn off the oven, crack the door open, and let the cheesecake cool inside for 30 minutes.
4. Remove from the oven and cool completely at room temperature. Refrigerate for at least 4 hours or overnight.

Step 4: Prepare the Blueberry Topping

1. In a small saucepan over medium heat, combine blueberries, sugar, cornstarch, and water.
2. Stir continuously until the mixture thickens and coats the back of a spoon.
3. Remove from heat and let cool before spreading over the chilled cheesecake layer.

Step 5: Assemble and Serve

1. Once the cheesecake is fully chilled, carefully remove it from the springform pan.
2. Spread the cooled blueberry topping evenly over the cheesecake layer.
3. Refrigerate for another hour before slicing for best results.