In a small saucepan over medium-low heat, gently heat oil until a slice of onion sizzles when added. Add half of the onions and cook, stirring occasionally, until deep golden brown, about 7-10 minutes. Using a slotted spoon, transfer to paper towels to drain, then season with salt to taste. The onions will start soft and crisp up as they cool. Repeat with the rest of the onions.