Preheat the oven to 200C/180C Fan/Gas 4 and line two large baking trays with baking paper.
Using an electric whisk, cream the sugars, peanut butter, butter and vanilla extract until pale and smooth. Add the eggs, one by one, mixing well after each addition so that the mix doesn’t curdle.
Whisk in the flour and bicarbonate of soda, then using a spatula or wooden spoon, fold through the oats until combined.
Place 40 heaped tablespoons of the mixture onto the trays and bake for 15 minutes or until golden brown. Allow to cool on the trays slightly before transferring to a wire rack to cool completely.
Sift the icing sugar into a large bowl and beat in the peanut butter and butter. Add a heaped tablespoon of the filling to the flat underside of 20 of the cookies and sandwich together with the remaining cookies.