Preheat your oven to 350°F (175°C) and gather your springform pan. Grease the bottom and sides to ensure easy removal later, then line the base with parchment paper.

In a mixing bowl, beat the cream cheese and sugar together using an electric mixer on medium speed until smooth and creamy, about 2-3 minutes. Gradually add in the egg white, mixing until fully incorporated.

In a separate bowl, whisk together the all-purpose flour, baking powder, baking soda, and salt until well combined.

In a large mixing bowl, beat the softened unsalted butter and sugar together until the mixture becomes light and fluffy, approximately 4-5 minutes. Add the whole egg, egg yolk, and vanilla extract, continuing to beat until thoroughly mixed.

Gradually add the dry ingredients to the butter mixture, alternating with the sour cream. Start and end with the dry ingredients, mixing on low speed until just combined.

Spread half of the batter into the prepared springform pan, ensuring an even layer. Spoon the cream cheese filling over the batter, followed by a generous scattering of raspberries. Dollop the remaining batter on top.

In a small bowl, mix together the sugar, flour, and softened butter to create a crumbly texture. Sprinkle this streusel topping uniformly over the batter.

Slide the cake into your preheated oven and bake for 40-45 minutes, or until a toothpick inserted in center comes out clean.

Once baked, allow the cake to cool in the pan for about 10 minutes. Then, carefully transfer it to a wire rack to cool completely.