2 tablespoons ginger beer OR ½ teaspoon ground cardamom
Place vegetable oil in fryer; cover and set temperature for 375ºF.
In large mixer bowl place butter and both sugars. Beat, scraping bowl often, until mixture resembles small pebbles (about 1 to 2 minutes). Add eggs, one at a time, beating well after each addition; add buttermilk and vanilla, mix well. In medium mixing bowl stir together flour, baking powder, salt, baking soda, and cardamom. Add dry ingredients to buttermilk mixture and mix until dough comes together. Dough is slightly sticky.
On well floured surface and using a well-floured rolling pin, roll out dough to ½ inch thick. Using a 3-inch biscuit cutter, cut out round rings of dough. Using a 1-inch cutter, cut center out of larger round. Reroll remaining dough and repeat cutting. Let donut rings and donut holes set on a cooling rack for 15 minutes.
Add about 6 donut rings to fryer at a time. Cover and fry for 1 minute; turn donuts over, continue frying 1 additional minute, or until golden brown. Remove from fryer and let drain on paper towel lined tray. Repeat with remaining dough rings and donut holes.
Meanwhile, in small bowl stir together confectioners’ sugar and ginger beer. Drizzle over donuts and donut holes. Let cool.