Preheat the oven to 325 degrees and line two large baking sheets with parchment paper. Set them aside for later.
Chop the pecans roughly using a sharp knife or a food processor. If you use a food processor, pulse 4-5 times. It's ok if there are a few larger pieces of pecans.
Cream the butter and brown sugar together in a large mixing bowl on medium speed using an electric mixer. Add both teaspoons vanilla extract. The mixture should have a smooth texture.
Slowly mix in the gluten-free flour, salt, and cardamom.
Once the flour is combined, hand-stir the chopped pecans into the dough.
Lay a sheet of plastic wrap on the counter and place the dough on top in a line. The line doesn't have to be perfect.
Roll the dough line up in the plastic wrap and secure both ends by twisting them. Use your hands to gently roll the dough like you would roll a rolling pin.
Chill the cookie dough roll in the refrigerator for 30 minutes.
Remove the cookie dough from the refrigerator and unwrap it from the plastic wrap.
Use a sharp knife to slice the dough into cookie rounds.
Line the baking sheet with the cookies and top each one with a pecan piece.
Bake in the oven for 14 minutes.
Remove from the oven and let the cookie cool completely on a wire rack.
Sprinkle the baked cookies with powdered sugar using a sifter.
Notes
Keep some pecans whole and place one on top of each cookie before baking.