Combine 3/4 cup sugar, eggs, egg yolks, and brandy in a large mixing bowl; beat until thick and lemon colored. Gradually add whipping cream; beat well.
Sift together flour and cardamom in a medium mixing bowl; add to sugar mixture, 1/2 cup at a time, stirring well after each addition. Cover and refrigerate overnight.
Turn out a small portion of dough onto a lightly floured surface; roll to 1/8-inch thickness. Cut into 3- x 2-inch diamonds; make a 3/4-inch lengthwise slit in the center of each, and gently pull one corner through as far as possible without tearing.
Drop 3 to 4 at a time into 4 inches of hot oil (375°). Cook 2 minutes, turning once or until golden brown. Drain on paper towels; sift powdered sugar over tops of cookies. Repeat procedure with remaining dough.