Preheat your oven to 350°F (175°C). Grease a 9-inch springform pan with butter or cooking spray, then line the bottom with parchment paper.

In a medium bowl, beat the softened cream cheese with 1/4 cup of sugar using an electric mixer until smooth and creamy, about 2 minutes. Add the egg white and mix until fully incorporated.

In a separate large bowl, whisk together 1.5 cups of all-purpose flour, 1/2 teaspoon baking powder, 1/2 teaspoon baking soda, and 1/4 teaspoon salt.

Cream 5.5 tablespoons of softened unsalted butter with 1/2 cup of sugar in a large mixing bowl until light and fluffy, around 3-4 minutes. Add in one large egg and one egg yolk along with 1 teaspoon of vanilla extract, mixing until just combined. Gradually add the dry flour mixture, alternating with 3/4 cup of sour cream.

Spread half of the cake batter evenly into the prepared springform pan. Pour the creamy filling over the batter, smoothing it out gently. Evenly distribute the raspberries on top of the cream cheese filling, then carefully spoon the remaining batter over the raspberries.

In a small bowl, combine 1/3 cup of sugar with 1/2 cup of flour before cutting in 3 tablespoons of chilled unsalted butter. Mix until crumbly. Sprinkle this streusel topping generously over the cake batter.

Transfer the pan to your preheated oven and bake for 40-45 minutes. It's done when a toothpick inserted into the center comes out clean and the top is a lovely golden brown.

Once baked, remove the coffee cake from the oven and allow it to cool in the pan for about 10 minutes. Carefully run a knife around the edges before releasing the springform clasp. Let the cake cool completely on a wire rack before slicing.