Stir together first 3 ingredients in a large glass bowl; let stand 5 minutes.
Stir in flour and next 3 ingredients until blended.
Pat or roll dough to 1/8-inch thickness; cut with a 2 1/2-inch round cutter. Let stand 45 minutes.
Pour oil to a depth of 2 inches into a Dutch oven; heat to 375°. Fry doughnuts, in batches, 1 minute on each side or until golden. Remove with a slotted spoon; drain on paper towels.
Roll doughnuts in powdered sugar.