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Sift together the flour, baking powder, baking soda and salt in a medium bowl.
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In the bowl of a stand mixer fitted with the paddle attachment, beat the peanut butter and butter on medium speed until creamy and smooth. Add the brown sugar and continue beating on medium until the mixture is light. Add the eggs, one at a time, beating well after each addition. With the mixer on low alternately add the dry ingredients and milk, beginning and ending with the flour mixture, and beating just until combined.
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Spread the batter evenly in the prepared pan. Sprinkle the topping evenly over the cake. Bake for 30-35 minutes, or until the cake is golden brown and a toothpick inserted in the center comes out clean. Transfer the pan to a wire rack and cool for at least 30 minutes before slicing and serving.