For the cake: Position an oven rack in the center of the oven, and preheat to 350 degrees F. Butter a 10-cup bundt pan. Sift the flour, baking powder, salt and baking soda together onto a piece of parchment or into a large bowl.
Beat the brown sugar, butter and peanut butter in a large bowl with an electric mixer on medium-high speed until the mixture is light and creamy, about 5 minutes. Scrape down the side of the bowl as needed. Add the eggs, 1 at a time, beating well after each addition. Continue beating until the mixture is light and creamy, about 2 minutes. Beat in the vanilla. Reduce the mixer speed to medium-low, and add the flour mixture in 3 additions and the milk in 2 additions, beginning and ending with the flour. Beat until just combined.
Pour half the batter into the prepared pan, then spoon the jelly in the center of the batter. Top with the remaining batter, and smooth out into an even layer. Bake until a toothpick inserted in the center comes out clean, 45 to 50 minutes. Let the cake cool in the pan for a few minutes, then invert onto a cooling rack to cool completely.
For the glaze: Beat the butter, peanut butter and confectioners' sugar until smooth. Spoon the glaze onto the cake, and spread to cover the top.
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