Preheat oven 375 degrees. Prepare a baking sheet with parchment paper. Combine gluten-free flour, almond flour, sugar, and salt in a large bowl. Cut in butter, add maple syrup, almond extract, and vanilla. Mix to form a dough.
Roll dough between 2 pieces of parchment paper about 1/4 inch thickness. Using the round cookie cutter, cut cookies out. Dip your cookie stamps into extra gluten-free flour, brush off excess. Press cookie stamps into the dough. Transfer cookies to the baking sheet, repeat the process and reroll scraps until all dough is used up.
Chill until dough for approximately 30 minutes in the refrigerator. Bake for 15 minutes or until golden. Allow cookies to cool for 2 minutes on baking sheet.Transfer to wire rack to cool completely.