1/2 cup unsalted butter, softened; more to butter the pan
3/4 cup unbleached all-purpose flour; more for the pan
3/4 cup honey-roasted peanuts
1/4 cup granulated sugar
1/2 cup old fashioned rolled oats (not steel cut or quick cooking)
1/2 tsp. baking powder
1/4 tsp. baking soda
1/4 tsp. table salt
2/3 cup packed light brown sugar
1/4 cup smooth salted peanut butter, preferably natural (if using unsalted peanut butter add a pinch of salt to the batter)
1 large egg, at room temperature
1/4 cup pure maple syrup
2 tsp. pure vanilla extract
Position a rack in the center of the oven and heat the oven to 350°F. Butter and flour an 8-inch square baking pan.
Grind the peanuts and granulated sugar in a food processor to the consistency of moist sand. In a small bowl, combine the flour, oats, baking powder, baking soda, and salt.
In a large bowl, beat the butter and brown sugar with an electric hand mixer on medium speed until light and fluffy, about 4 minutes. Beat in the peanut butter until smooth, and then beat in the egg. Add the maple syrup and vanilla; beat until light, smooth, and fluffy.
With the mixer on low speed, mix in the flour mixture. Add the ground peanut mixture and using a wooden spatula, stir until combined. Spread into the prepared pan.
Bake until puffed and browned and a toothpick inserted into the center comes out clean, about 30 minutes. Cool in the pan on a rack for 10 minutes. Run a thin knife along the edge, turn out of the pan, invert onto the rack, and continue to cool until barely warm, about 1 hour.