Preheat oven to 425 degrees F. On a large rimmed baking sheet, toss radishes, 2 tablespoons olive oil, 1/2 teaspoon kosher salt, and 1/2 teaspoon pepper. Arrange radishes in a single layer, cut sides down. Roast 15-20 minutes, until cut sides are light golden brown and radishes are crisp-tender. (Turn and continue roasting for an additional 5 minutes or so if you prefer a softer texture.)
While radishes are roasting, combine Dijon mustard, lemon zest and juice, shallot, and tarragon in a small bowl. Pour in extra-virgin olive oil in a steady stream while whisking, until dressing is emulsified. Season to taste with salt and pepper.
Let radishes cool slightly, place in a serving bowl, and gently toss with vinaigrette (you might not need all of the dressing). Serve slightly warm, or at room temperature, garnished with additional lemon zest, if desired.