Thinly slice onions and separate into rings.
Place flour in a bag, add onions, and shake to coat evenly with flour.
In a deep 2 1/2- to 3-quart pan over high heat, bring 1 1/2 inches oil to 300°F on a deep-frying thermometer.
Add onions, about 1/4 at a time; cook, stirring often, until golden, about 5 minutes.
Oil temperature will drop at first but rise again as onions brown; regulate heat accordingly.
With a slotted spoon, lift out onions and drain on paper towels (discard any scorched bits).
Serve warm, piled in a napkin-lined basket or on a plate; sprinkle with salt.
Or let cool completely, package airtight, and refrigerate for up to 3 days.
To reheat, spread in a single layer in a 10- by 15-inch rimmed baking pan and heat in a 350° oven for 2 to 3 minutes.