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TO MAKE THE CAKE: Place 1 oven rack in the top third of the oven and the second in the bottom third.
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Preheat the oven to 350F.
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Line three 9-inch cake pans with parchment paper rounds, grease with butter or cooking spray, dust the pans with flour, and knock out the excess.
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Using an electric mixer fitted with the paddle attachment, cream the 1 cup butter and granulated sugar on medium-high speed until light and fluffy, about 3 minutes.
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Use a rubber spatula to scrape down the sides of the bowl.
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Add the eggs all at once and beat on medium speed until combined.
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In a bowl, stir together the flour, baking powder, and salt.
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Stir the 2 teaspoons vanilla into the milk.
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Add the flour mixture and milk in alternating batches, beginning and ending with flour.
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After each addition, mix on low speed just to combine the ingredients.
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Stir in the peanut butter chips.
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Divide the cake batter evenly among the prepared cake pans.
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Set 2 layers on the top rack and the third on the lower rack.
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Stagger the cake layers on the oven racks so that no layer is directly over another.
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Bake until the cake is golden, firm to the touch, and a toothpick inserted into the middle comes out clean, 25 to 30 minutes.
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Monitor the layers carefully for doneness; each one may be done at a different time.
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Cool the layers in their pans about 10 minutes; unmold onto wire racks to cool completely.
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TO MAKE THE FROSTING: Using an electric mixer fitted with the paddle attachment, beat the 1 cup butter and peanut butter on medium speed until fluffy, about 3 minutes.
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Add the powdered sugar, cream, and the 2 teaspoons vanilla and beat on medium speed until light and fluffy, about 2 more minutes.
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TO ASSEMBLE THE CAKE: Place 1 cake layer on a serving plate and spread the top with half of the jam.
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Repeat with a second layer.
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Stack the final cake layer on top of the first 2 and cover the cakes top and sides with frosting.
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Press the chopped peanuts around the sides of the frosted cake.