In a large skillet, heat oil over medium-high. Add onion; season with salt and pepper. Cook, stirring frequently, until onion is tender and golden, 6 to 8 minutes.
Add as many greens to skillet as will fit; season with salt and pepper. Cook until wilted, tossing and adding more greens as room becomes available, 2 to 3 minutes. Stir in vinegar; season with salt and pepper, and serve.
Mustard greens don't last long, so buy only what you plan to use within a few days. To clean, fill a bowl with cold water, and add greens, swishing gently. Scoop out greens. Drain water off. Repeat with fresh water until no grit remains at the bottom of the bowl. Dry with a salad spinner, or pat with paper towels. Store washed greens in a resealable plastic bag lined with dry paper towels in the refrigerator up to 1 day.
I thought this was a great new alternative to how we usually make our greens (savory/tangy). I only had yellow onions so I added some honey and got really good results. We ate this with some potatoes, gardein "beef" tips and a dijon sauce.