Cut onion crosswise into 1/2-inch-thick slices, and separate into rings. Use 16 of the largest rings; reserve remaining onion for another use. Combine flour and next 3 ingredients (through pepper) in a medium bowl. Stir in beer and egg white (batter will be thick). Heat 1 tablespoon oil in a large nonstick skillet over medium-high heat. Dip 5 onion rings in batter, letting excess drip off. Add onion rings to pan; cook 2 minutes on each side or until golden. Place onion rings on a jelly-roll pan. Repeat procedure of dipping onion rings in batter and cooking in remaining oil twice, ending with 6 rings. Coat onion rings with cooking spray.
Bake at 400° for 10 minutes or until crisp. Serve rings with ketchup, if desired.