Preheat oven to 350 degrees F. Prepare two baking sheets lined with parchment paper.
In a large bowl, cream butter and sugar. Add flour and continue to mix until a soft dough ball forms (it's OK if it is a bit crumbly).
Roll dough 1/3-inch thick on a surface dusted with powdered sugar with a well-dusted rolling pin. Cut into rounds or any shape you want and place on prepared baking sheets.
Bake for 16-18 minutes, or until cookies are pale golden brown. Let cool on baking sheets. Ice with buttercream.
To make brown butter:
Place just over 1 cup of butter in a small and and set heat to medium. Cook until the solids turn a little brown and a nutty smell comes up. Remove from heat and stir in pan until the solids are a bit browner. Pour butter in a dish and cool in fridge or freezer.
Brown Butter Shortbread with Butter Buttercream https://cultureatz.com/brown-butter-shortbread-with-butter-buttercream-3/