Preheat oven to 350°F and line a large baking sheet with parchment paper.
In a large bowl or stand mixer fitted with a paddle attachment, combine all of the ingredients and mix well, scraping down the sides as needed. The dough will be very sticky.
Using a small cookie scoop, scoop out the dough and drop onto the prepared baking sheet about 2 inches apart. If you use a medium cookie scoop, add 1 to 2 minutes to the bake time.
Bake for 8 minutes to start, cookies should have a thin film on top and the batter should no longer be glossy, should still be able to see small ripples of darker batter. DO NOT OVERBAKE THESE COOKIES. They will cook up fast and can dry out easily if cooked too long. Every oven is different, so do a few in a test batch to see how long they need.
While the cookies are baking, beat together the peanut butter, powdered sugar, and vanilla in a large mixing bowl.
Once the cookies come out of the oven, use a medium cookie scoop to portion out the peanut butter mixture. Divide each scoopful in half and roll into a ball then gently flatten and press into the top of the hot cookies.
Transfer to a cooling rack.
Melt the melting wafers in a medium bowl at 30-second intervals until fully melted, then spread over the tops of the peanut butter mixture on the cookies and allow to set.