Preheat the oven to 350 degrees F. Cut a piece of foil 9 by 20-inches. Butter the corners and sides of a 9-by-13-inch baking pan. Line the pan with the foil so that the excess hangs over at each of the short sides of the pan.
Whisk the flour in a medium bowl with the baking powder, baking soda and salt. Whisk in 1/2 cup peanuts.
Put the melted butter in a large bowl and use a rubber spatula to stir in the sugars. Stir vigorously, mashing the brown sugar lumps with the spatula, so that the mixture is well combined and creamy. Using the rubber spatula, stir in the peanut butter, again making sure the mixture is well combined. Stir in the eggs and vanilla. Fold in the flour mixture until just combined.
Scrape the batter into the prepared pan. Press the back of a spoon or a curved rubber spatula into the batter to make little wells all over the batter, making sure not to push down to the bottom of the pan. Spoon the jam into the wells, making sure the jam is distributed evenly across the pan. Use a knife to pull the jam through the peanut butter mixture-it won't exactly ribbon, you will end up with some chunks of jam throughout. Sprinkle the remaining 1/2 cup chopped peanuts over the top.
Bake until a toothpick inserted in the center of a non-jammy spot comes out clean, about 35 minutes. Cool completely on a rack, about 1 hour.
When the bar has cooled completely, place a lightweight cutting board or a baking rack over the top of the pan. Flip and set on the counter. Gently pull the pan from the foil and the foil from the pan to remove. Gently peel the foil off the bar. Place another lightweight cutting board on top, and flip the bar right-side-up. For easier slicing, wrap with plastic wrap, and let sit at room temperature overnight. Cut into forty eight 1 1/2-inch squares.