Step 1: Preheat the Oven. Preheat your oven to 350°F (175°C). Grease your 9-inch round baking pan and line the bottom with parchment paper for easy removal.
Step 2: Make the Cake Batter. In a large mixing bowl, combine the grated frozen unsalted butter and sugar. Use an electric mixer to cream them together until light and fluffy. Add the egg, sour cream, and vanilla extract, mixing until well combined.
Step 3: Combine Dry Ingredients. In another bowl, whisk together the flour, baking powder, baking soda, and a pinch of salt. Gradually add the dry ingredients to the wet mixture, mixing until just combined. Be careful not to overmix; a few lumps are okay.
Step 4: Prepare the Cheesecake Filling. In a separate bowl, beat the room temperature cream cheese until smooth. Add the ¼ cup sugar, 1 egg, and 1 teaspoon of vanilla extract, mixing until creamy and well combined.
Step 5: Assemble the Cake. Pour half of the cake batter into the prepared pan, spreading it evenly. Then, add the cheesecake filling on top, smoothing it out gently. Sprinkle the mixed berries over the cheesecake layer, and then dollop the remaining cake batter on top, spreading it gently to cover the berries.
Step 6: Make the Streusel Topping. In a small bowl, combine the slivered almonds with a bit of leftover cake batter (or butter and flour) to create a streusel topping. Sprinkle this mixture over the cake.
Step 7: Bake the Cake. Bake in the preheated oven for about 40 to 45 minutes, or until a toothpick inserted into the center comes out clean. The top should be golden brown and the cheesecake layer should be set.
Step 8: Cool and Serve. Once baked, remove the cake from the oven and let it cool in the pan for about 10 minutes. Carefully transfer it to a wire rack to cool completely. Serve it plain or with a drizzle of raspberry jam for an extra touch.