Heat oil in a heavy saucepan or deep fryer to 350oF.
Clean and trim artichokes to leave only the artichoke hearts. Cut artichoke hearts in halves or quarters, depending on size. Set aside.
To prepare the batter, begin by beating egg and beer together. Continue beating and add salt, garlic salt, flour, Bisquick, and baking powder. Stir in onion and parsley.
Add prepared artichoke pieces to batter. If batter seems too thin, add a little flour.
Deep fry in hot oil, turning artichoke pieces until they are browned. Drain on paper towels. Sprinkle with salt if desired.