Place your caster and light brown sugar is a bowl. Add your melted butter and mix throughly until combined.
Add in your egg and vanilla and mix in until combined.
Next add your peanut butter. Using an electric handmixer. Mix until smooth and combined.
Then add in your gluten free flour, bicarbonate of soda and optionally a 1/4 tsp of xanthan gum. Mix together until fully combined.
Chill in the fridge for 1-2 hours (cover the bowl with cling film). You can chill for longer too if you want to make the dough in advance.
Preheat your oven to 160C Fan / 180C and prepare 2 large baking trays with baking paper.
Once the dough has chilled, remove from the fridge and roll into balls (mine weighed about 35g each).
This step is optional: put your granulated sugar onto a plate and gently roll each dough ball in it. This will give it a lovely sparkle and crunch when it comes out the oven. You can also push in a few small pieces of peanut into the top of each ball - optional once more.
Place on your baking tray (leave gaps between them as they spread) and bake in the oven for about 15 minutes.
Remove from the oven and allow them to cool on the baking tray. Move over to a cooling rack to finish cooling completely.
For the icing, place your butter in a stand mixer (or use an electric hand whisk), mix on a medium speed for a minute or so.
Add all the other ingredients and mix briefly on a low speed (so icing sugar doesn't fly out) and then up to a high speed until combined and the right consistency for you. This usually takes a further 2 minutes.
If the icing isn't thick enough, just add a small amount more of icing sugar and mix it in until it's the thickness you want. It should be nice and easily spreadable.
To construct your cookie sandwiches, plonk a large blob of peanut butter icing in the middle of one of your cookies (the back of it of course!) Then using the other cookie, squash it down until the icing is just visible from the sides. Repeat with all your cookies.