Using a stand mixer, beat together softened butter and sugar until light and fluffy. Add the vanilla extract.
In a separate bowl, sift together GF plain flour, cornstarch and rice flour.
Gently combine sifted flours to the butter mixture in 3 parts until incorporated. Add a pinch of salt.
Cover the dough with plastic wrap and refrigerate for half an hour until firm.
Roll 10g of the mixture into balls. Place the balls on large baking trays lined with parchment paper, and press the tops slightly with a floured fork.
Bake in a preheated oven at 180*C for about 15 minutes. Transfer to a wire rack to cool.
Make the strawberry buttercream.
Cut the strawberries into pieces, and place them in a small saucepan. Cover with water and cook on medium heat until the strawberries are soft and water has been fully absorbed. Push the strawberries through a strainer. Set aside to cool completely.
Place the softened butter, icing sugar, strawberry liquid, strawberry extract and a pinch of salt in a medium bowl and, using either hand or stand mixer, beat until light and fluffy.
Pipe strawberry buttercream onto the flat side of the cooled cookies and top with another cookie.