Position a rack in the center of the oven and preheat to 350 degrees . Line an 8-inch square baking pan with an 8x13 inch sheet of parchment, letting the excess hang over.
Using a food processor, pulse the peanuts until chopped. Transfer to a medium bowl.
In the processor bowl (no need to clean), mix the 2 flours, the brown sugar and salt. Add the butter; pulse until the mixture resembles coarse meal. Add the peanut butter and vanilla; process until crumbly. Measure out 2/3 cup of the crumb mixture; transfer to the bowl of peanuts.
Dump the remaining crumb mixture into the prepared pan and pan down firmly (it doesn't have to be perfectly even). Spoon the jam on top and spread to within 1/2 inch of the edges. Sprinkle the peanut-crumb mixture evenly over the top, going all the way to the edges of the pan.
Bake until the top is golden-brown and the jam is bubbling, about 45 minutes. (If browning too quickly on top, lay a sheet of foil loosely over the pan.) Transfer the pan to a rack to cool completely.
Grasp the parchment and gently lift the entire dessert out of the pan. Place on a cutting board and cut into 16 squares.