Preparation: Preheat the oven to 350°F (175°C). Grease a 9-inch springform pan thoroughly and line the bottom with parchment paper. This step is crucial for ensuring the cake does not stick to the pan and can be removed easily after baking.

Cream Cheese Layer: In a mixing bowl, combine the softened cream cheese with ¼ cup of granulated sugar and ½ teaspoon of pure vanilla extract. Blend these ingredients on a medium-low speed until a creamy consistency is achieved. Add the egg white to the mixture, blending on low speed until just combined. This layer will contribute a rich, creamy texture to the cake.

Cake Base Preparation: In a separate bowl, sift together the all-purpose flour, baking powder, baking soda, and salt. In another bowl, cream together the 5.5 tablespoons of unsalted butter and ½ cup of granulated sugar on medium-low speed until light and fluffy. Add the whole egg, egg yolk, and 1 teaspoon of pure vanilla extract, blending well after each addition. Gradually alternate the addition of the dry ingredients with the ¾ cup of sour cream to the butter mixture, ensuring a smooth and uniform batter. Spread this batter evenly into the prepared springform pan. Scatter 1/3 cup of the fresh blueberries evenly over the batter.

Assembling: Gently spread the cream cheese mixture over the cake base, ensuring an even layer. Distribute the remaining blueberries atop the cream cheese layer.

Streusel Topping: Combine 1/3 cup of granulated sugar, ½ cup of all-purpose flour, and 3 tablespoons of chilled, diced unsalted butter in a bowl. Work these ingredients together using a fork or pastry blender until the mixture resembles coarse crumbs. Evenly sprinkle this streusel topping over the cake.

Baking: Bake the cake in the preheated oven for approximately 40-45 minutes, or until a cake tester inserted into the center comes out clean. If the cake begins to brown excessively, cover the top with aluminum foil to prevent overbrowning.

Cooling: Upon completion of baking, remove the cake from the oven and allow it to cool on a wire rack. Before releasing the cake from the springform pan, run a thin knife around the edges of the cake to separate it from the sides of the pan. This ensures the cake can be removed without breaking.

Storage: It is recommended to store the cake in a refrigerated environment, within an airtight container, to maintain its freshness and flavor.