1Cut onions into 1/2-inch slices; separate into rings. Set aside. In medium bowl, stir together 1 1/4 cups of the Bisquick mix and the sugar. In small bowl, mix buttermilk and beer; add to Bisquick mixture, stirring with whisk until smooth.
2In deep fryer or 3-quart heavy saucepan, heat 2 inches oil to 375°F. In large resealable freezer plastic bag, place onion rings and remaining 1/2 cup Bisquick mix. Seal bag and shake to coat. Dip each onion ring in batter, coating well. Carefully drop onion rings, in batches, into hot oil. Fry 4 minutes, turning occasionally, until golden; drain on paper towels. Serve hot.