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Step 1
Position a rack in the center of your oven and preheat the oven to 350.F. Butter or coat an 8-inch square baking pan with nonstick spray. Line the pan with a strip of parchment paper that hangs over two of the edges.
Step 2
In a large bowl, whisk the brown sugar and eggs until pale and foamy, about 1 minute. Add the sour cream, butter, vanilla, and salt. Whisk until smooth and emulsified.
Step 3
Add the flour, baking powder, and baking soda to the bowl. Whisk until well-combined and smooth.
Step 4
Use your fingers to break up the cream cheese into teaspoon-size pieces and scatter them over the top of the batter. Fold in the cream cheese and ½ cup (80g) of the berries.
Step 5
Pour the batter into the prepared pan, tap the pan gently on the counter to release any air bubbles, and smooth the top of the batter with an offset spatula. Scatter the remaining berries over the top and sprinkle with the turbinado sugar.
Step 6
Bake the cake until puffed and golden, and a tester inserted into the center comes out clean, 30 to 45 minutes. Set the cake on a rack to cool for about 15 minutes. Then use the parchment paper to lift the cake out of the pan and set it on the rack to cool completely. Serve warm or at room temperature. (Store the cake, wrapped tightly, in the fridge, for up to three days.)
Step 7
Cranberry cream cheese cake: Substitute 1 cup (100g) fresh or frozen whole cranberries for the mixed berries. Fold half into the batter and sprinkle half on top.
Step 8
Apricot and berry cream cheese cake: Substitute a combination of 1 cup sliced apricots (170g) and 1/2 cup (80g) berries for the mixed berries. Make sure to save a few slices of apricots for the top.
Step 9
Loaf: Fold 1 1/4 cups (200g) berries into the batter and sprinkle 1/4 cup (40g) over the top. Bake the cake in a 9 x 5 x 3-inch loaf pan until puffed and golden, and a skewer inserted into the center comes out clean, 50 to 60 minutes.
Step 10
Round: Bake in a 9-inch round pan until puffed and golden, and a tester inserted into the center comes out clean, 35 to 45 minutes.