In a large mixing bowl (preferably in an electric mixer), cream together butter and sugar until smooth, about 3 minutes. Beat in eggs, one at a time.
In a separate bowl, add in the flours, salt, cardamom and zest. Whisk to incorporate and add to the wet ingredients while mixer is on low, about 1/3 cup of dry ingredients at a time.
Scrape sides and beat again to ensure it's well mixed, but be careful to not over mix. Cover dough and chill dough for at least one hour (or overnight).
Preheat oven to 325 degrees F.
Roll out dough on floured surface, 1/2 inch thick. Cut into shapes with any cookie cutter. Place cookies 1 inch apart on cookie sheets lined with parchment paper.
Bake 6 to 8 minutes in preheated oven and remove just before the edges start to brown. Cool completely.
Dust cookies with powdered sugar and store in airtight container for up to 5 days.