In a small saucepan, melt the butter over medium heat; cool slightly.
In a medium mixing bowl, beat eggs with an electric mixer on medium speed for 1 minute. Add sugar; beat about 3 minutes or till sugar is almost dissolved. (Do not overbeat.) Stir the cooled butter, cardamom and vanilla into egg mixture.
In a small mixing bowl, combine flour and cornstarch. Add flour mixture to egg mixture. Stir just till smooth. (Dough will be sticky enough to be dropped by spoon onto heated krumkake iron.)
Heat a krumkake iron on the range top over medium-high heat. Test iron with a few drops of water; if they "jump," iron is correct temperature. For a 6-inch iron, drop a slightly rounded 1 tablespoon measure of the batter onto the hot, ungreased iron. Close gently but firmly. (Do not squeeze.) Cook over medium-high heat 15 to 20 seconds or till lightly golden. Turn iron and cook the other side about 15 seconds more. (Keep iron over heat at all times.) Open the iron carefully. Loosen cookie with a narrow spatula; invert onto a wire rack. Immediately roll the cookie around a metal or wooden cone or cylinder till it holds the shape.
Reheat the iron and repeat with remaining batter. If cookies brown too quickly, reduce heat to medium. Cool rolled cookies on a wire rack. The rolls or cones can be served plain or, if you like, pipe the cookie cones full of sweetened whipped cream and serve immediately. Makes about 36 cookies.