In a medium bowl, stir together flour, cornstarch, 2 tablespoons granulated sugar, cinnamon and cardamom; set aside.
In a large mixing bowl, beat butter with an electric mixer on low speed for 30 seconds. Add the brown sugar. Beat until combined, scraping sides of bowl occasionally. Beat in as much of the flour mixture as you can with the mixer. Stir in any remaining flour mixture. If necessary, chill in the refrigerator for 30 minutes or until easy to handle.
Shape dough into 10-inch-long roll. Wrap in plastic wrap or waxed paper; chill in refrigerator at least 2 hours or up to 24 hours or until firm enough to slice.
With a serrated knife, cut roll into 1/4- to 1/2-inch-thick slices. Place slices 1 inch apart on ungreased cookie sheets. Reshape roll as necessary. Sprinkle slices with additional granulated sugar. Bake cookies in a 350 degree F oven for 8 to 10 minutes for the 1/4-inch thick cookies or 12 to 14 minutes for the 1/2-inch thick cookies or until bottom just starts to brown.
Cool on cookie sheets for 1 minute. Transfer cookies to wire racks; cool. If you like, wrap cookies in pairs, back to back, or individually with plastic wrap. Makes about 3 dozen 1/4-inch thick cookies or 20, 1/2-inch thick cookies.