Thinly slice onion. Place in bottom of a large salad bowl.
With a paring knife, cut off peel and white pith of oranges. Over the salad bowl, section the oranges by cutting the segments in between the membranes (this is called supreming). Squeeze the remains over the bowl.
Give two generous turns of olive oil over the bowl, about 3 tablespoons. Add a pinch of salt and several cranks of ground black pepper to taste. Add one splash of red wine vinegar to taste.
Toss everything together, taste dressing, and adjust salt, pepper, and vinegar to your preference. Let this onion and orange mixture sit until ready to serve. The longer the onion sit in the orange juice, the more mellow they become.
Place the mixed baby greens on top of the onions and oranges, and toss to evenly coat with the dressing.