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Whisk together flour, baking powder, baking soda, and salt in a bowl.
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Stir together sour cream and vanilla in a small bowl.
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Beat together butter and sugar in a large bowl with an electric mixer at medium-high speed until pale and fluffy, about 5 minutes. Add egg and beat until well blended.
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At low speed, mix in flour mixture in 3 batches, alternating with sour-cream mixture and mixing until just combined.
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Gently fold in blueberries.
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Spoon batter into pan, smoothing top (preferably with an offset spatula). Crumble half of topping evenly over batter.
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Bake 25 minutes, then remove from oven and crumble remaining topping evenly over cake. Bake until a wooden pick inserted into center comes out clean, about 25 minutes more. Cool in pan 10 minutes. Lift out cake using foil and cool completely on rack.