If using fresh cardamom, grind pods into a fine powder.
Beat butter, sugar, on low speed until the sugar is incorporated, and then increase to medium speed and continue to beat until creamed, about 30 seconds. Scrape the sides.
Add the flour and cardamom and mix on low speed until the dough comes together in medium-sized chunks and you do not see any flour streaks in the bowl. Do not overmix.
Press the dough together using a spatula or your hands, then turn onto a sheet of plastic wrap. Use the plastic wrap to help shape the dough into a disk. Wrap tightly with the plastic wrap and refrigerate for 30 minutes.
Preheat oven to 325 and line a baking sheet with parchment paper.
Remove dough from the refrigerator. Unwrap the dough and place it between two sheets of parchment paper. Roll ½-inch thick, then cut out with cookie cutters. Place the cookies onto a parchment-lined plate and put in the freezer for 10-15 minutes.
Transfer the dough onto your baking sheet and bake for 20-22 minutes, or until very lightly golden. Remove from the oven and cool for 5 minutes in the pan, then remove to a cooling rack to cool completely.