Heat oven to 400° F. Heat 1 tablespoon of the oil in a large ovenproof skillet over medium-high heat.
Season the pork with ¼ teaspoon each salt and pepper. Cook, turning, until browned, 5 to 6 minutes.
Transfer the skillet to oven and roast until the pork is cooked through, 12 to 15 minutes. Let rest for at least 5 minutes before slicing.
Meanwhile, on a rimmed baking sheet, toss the asparagus and shallots with 1 tablespoon oil and ¼ teaspoon each salt and pepper.
Arrange the vegetables in a single layer and roast, tossing once, until tender, 12 to 15 minutes.
In a bowl, whisk together the vinegar, mustard, and remaining ⅓ cup of oil. Serve the pork with the vegetables and drizzle with the vinaigrette.