Cut onion into 1/4-inch-thick slices, and separate into rings. Select largest 12 rings, reserving remaining onion slices for another use.
Whisk together buttermilk, beer, and egg white in a small bowl until blended.
Dredge onion rings in flour; dip into buttermilk mixture, coating well. Dredge again in flour, and place on a baking sheet.
Heat 2 tsp. oil in a 10-inch skillet over medium-high heat. Tilt pan to coat bottom of skillet. Add 4 onion rings to skillet, and cook 1 minute on each side or until golden. Wipe skillet clean. Repeat procedure twice with remaining onion rings and oil. Place fried onion rings on an aluminum foil-lined baking sheet coated with cooking spray.
Bake at 400° for 3 minutes. Turn onion rings, and bake 3 more minutes. Remove from oven, and sprinkle with salt. Serve immediately.