Heat oil in a home deep-fryer to 375 degrees. If you do not have a home fryer, use a large pot and a fry basket. Fry onions in multiple batches. Use a thermometer to make sure temperature returns to 375 degrees between batches.
Slice onions as thin as possible using a mandoline or cut with a knife.
Make an egg wash by combining milk and eggs. Put onions in colander set over a bowl. Pour egg wash over onions. Allow the wash to drip out. Onions should be completely covered, but not too wet. Use egg wash that seeps into bowl if needed or discard.
Dredge in flour so onions are lightly covered.
Fry according to manufacturer's instructions on home fryer. If using a pot, place a few cups of prepared onions into fryer basket and slowly lower into pot.
Onions will make the oil bubble and foam up considerably; lowering the basket slowly will prevent oil from dangerously spilling over the sides of the pot. Fry onions until golden brown, about 1 1/2 to 2 minutes, moving constantly so they brown evenly. Remove from oil and season with salt to taste. Serve immediately.