In a large bowl combine buttermilk and baking soda; season well with salt and pepper. Peel onions and slice thinly, no thicker than 1/4-inch; a mandoline works well. Add to buttermilk mixture and stir well to submerge all onions. Set aside, unrefrigerated, for 2 hours.
In a deep-fryer or heavy, deep pot, heat at least 1 quart oil to 375 degrees F. Working in batches, place about 1/6 of flour in a large bowl. With your hands, remove about 1/6 of onions from buttermilk. Don't let the liquid run off. Add to flour and mix vigorously with your hands until onions are well-coated. Separate them by hand and lay them in a deep-fry basket. Lower into hot oil, maintaining temperature. Stir every 2 minutes. When onions are golden brown and crisp, about 6 minutes, drain on paper towels and sprinkle with salt. Keep warm in a 200 degree F oven while you finish the rest.