Whisk together mustard, vinegar, and 1 tablespoon oil in a medium bowl. Season with salt and pepper.
Heat remaining 1 tablespoon oil in a large skillet over medium heat. Add asparagus, and season with salt and pepper. Reduce heat to medium-low. Cook, stirring frequently, until asparagus are just tender, 10 to 12 minutes. (If the spears begin to brown, reduce heat to low.)
Transfer asparagus to a serving dish. Drizzle with the vinaigrette, toss, and serve immediately.