Position an oven rack in the center of the oven, and preheat to 350 degrees F. Butter a 9-by-13-inch baking dish.
For the cake: Whisk the flour, baking powder, salt and baking soda together in a large bowl.
Beat the brown sugar, butter and peanut butter in another 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 the batter into the prepared baking dish. Spoon dollops of the jelly all over the top, and swirl with the back of a spoon.
For the topping: Mix together the flour, brown sugar, peanuts and salt in a small bowl to combine. Add the butter, and mix thoroughly with your fingers or a fork until it has been evenly distributed and incorporated into the flour mixture. Scatter the topping over the batter. Bake until the cake is golden brown and a toothpick inserted in the center comes out clean, 50 to 60 minutes. Let cool in the baking dish on a rack. Dust with confectioners' sugar, cut and serve.
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