Preheat oven to 350 degrees F.
Cream the butter and peanut butter together in a large mixer on high. Add the sugar, brown sugar and vanilla and continue to beat until the mixture is fluffy. Add the egg and beat until combined. Mix the flour, baking soda, baking powder, and oats together in a separate bowl and add to the butter mixture. Mix until well combined.
Place the batter onto a sheet pan by the tablespoonful, leaving about 2 inches between each cookie. Bake in the top half of the oven until the cookies are golden, about 10 minutes. Remove and let cool.
When the cookies are completely cool, put a teaspoonful of the butter cream or simply just some peanut butter and strawberry jelly, or chocolate-hazelnut spread into the center of half of the cookies. Top with the remaining cookies, pressing down until the filling squeezes out a bit. Refrigerate until ready to serve.
Pinch salt Cream the butter and peanut butter together using an electric mixer. Add the sugar and molasses and beat until thick and creamy, about 2 minutes. Add the heavy cream and salt and beat one additional minute. Spread on the cookies immediately.