Mix together the flour, baking powder, baking soda and salt.
In a mixing bowl beat the softened butter, peanut butter and both sugars until light and creamy. Add egg and stir until smooth, then beat in the vanilla extract.
Add the flour mixture to the butter mixture and stir until smooth, then stir in the peanuts and oats.
Divide dough into 12 rounds. Put them on a dinner plate and chill until firm enough to roll into balls. Roll into balls and press into disks.
Keep chilled until ready to bake.
To bake, preheat oven to 325 degrees F.
Arrange disks on a parchment lined baking sheet and bake for about 12-15 minutes or until cookies start to brown around the edges.
Remove from oven and put a Reese's Thin in the center of each cookie. Sprinkle the sea salt. You can do this right away, or you can wait and let the chocolate set a bit before adding the salt. The crystals stand out more if you let the chocolate set.
Let the cookies cool on the sheet for 10 minutes, then transfer to a wire rack.
Alternatively, let the cookies cool on brown paper sacks for about 10 minutes, then transfer to a wire rack to finish cooling.