Heat oil in a small saucepan placed over medium-low heat. A slice of onion should just sizzle a bit when added to the hot oil. Add 1/2 of the onions and cook, stirring occasionally, until the onions are a deep golden brown, about 7-10 minutes. Remove with slotted spoon to paper towels to drain, and salt to taste. Onions will be soft at first and will crisp as they cool. Repeat with remaining onions.
