1. In a large skillet, heat the oil over medium heat. Add the onion and sauté until translucent. Reduce the heat to low and continue to cook, stirring occasionally, until the onion begins to caramelize, about 15 minutes.
2. Add the cherry tomatoes and, with the back of a spoon, break 4 to 5 tomatoes to release their juices. Add the vinegar, and salt and pepper to taste and cook, stirring occasionally, 3 minutes longer.
3. Meanwhile, toss the greens with the mustard dressing. Pile the greens onto 4 individual salad plates and spoon some of the hot tomato-onion mixture alongside. Serve immediately.