Peel the onion. Slice it into thin slices and separate the slices into rings.
Heat the olive oil in a large 12-inch nonstick skillet over medium heat until it shimmers, about 2 minutes.
Add the onion rings. Use a wooden spoon to spread them evenly in the skillet. Sprinkle them with salt.
Cook the onions uncovered, stirring frequently, until they are soft and golden brown, about 10 minutes.
Serve immediately.
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Notes
It's tempting to crank the heat up when cooking onions. But, while we don't necessarily try to get them super browned and caramelized in this recipe (here's a recipe for caramelized onions), we do want them evenly soft and golden, with some brown bits. So, while we don't need to cook them over low heat, we should certainly stick with medium heat and avoid the temptation to cook them over medium-high heat.
Be ready for the onions to lose quite a bit of volume as you slowly cook them! They end up being about half the volume they were before cooking. So, take that into account when deciding how much to make.
You can keep the leftovers in an airtight container in the fridge for up to 4 days. When ready to use them, reheat them in the microwave at 50% power. They will be just as good as when freshly made. You can also freeze the cooled leftovers for up to three months. I like to freeze them in single-serve containers.