Preheat oven to 350. Lightly grease or line baking sheets with parchment paper.
In a mixing bowl, cream together butter and peanut nutter until smooth and fluffy.
Add the sugars, the egg, the milk and vanilla. Mix well.
Slowly add dry ingredients and mix until thoroughly combined.
Pour some sugar in a shallow dish. Roll cookie dough into 1 inch balls and roll each each ball around in the sugar until coated on all sides.
Space sugary cookie balls evenly on your baking sheet making sure to leave enough room for them to spread out.
Bake for 10-12 minutes. The cookies will be puffy straight out of the oven, but will settle down as they cool.
Allow cookies to cool for 5 minutes on the pan, then move them to cooling racks. Lightly cover the cookies with a sheet of plastic wrap and leave them alone.
In a large microwaveable bowl, melt together chocolate chips, vanilla, corn syrup, and heavy cream in 30 second increments until chips are melted and stirring the mixture gives you smooth, liquid chocolate.
Let cookie mixture cool completely to room temperature, then cover and stick your bowl in the fridge 10-15 minutes. Frosting should be thick but spreadable.
Spoon frosting generously on the bottoms of half your cookies. Top with remaining cookies to complete the sandwiches. Serve with lots of milk.