Preheat the oven to 425˚F (220˚C).
Spread the radishes on a baking sheet and the asparagus on a second baking sheet. Drizzle both with oil and season with salt and pepper, tossing to evenly coat the vegetables. Spread the vegetables in an even, single layer.
Roast the radishes for 10 minutes. Give them a shake, then add the pan of asparagus to the oven.
Roast until both the radishes and asparagus are lightly golden and tender, 12 to 14 minutes.
While the vegetables are roasting, whisk together the vinegar and mustard, then slowly whisk in the 3 tablespoons oil. Season to taste with salt and pepper.
Transfer the radishes and asparagus to a serving platter. Lightly drizzle with the vinaigrette and sprinkle with tarragon. Serve immediately with extra vinaigrette on the side.