1. Place a large heavy baking sheet in oven. Preheat the oven to 400° (keep the baking sheet in oven as it preheats).
2. Combine potatoes, 1 1/2 tablespoons oil, garlic, and thyme in a medium bowl; toss to coat. Arrange the potato mixture on preheated baking sheet, and sprinkle with 1/2 teaspoon salt and 1/2 teaspoon black pepper. Bake at 400° for 30 minutes or until browned and tender, turning after 20 minutes.
3. Combine remaining 1 1/2 tablespoons oil, remaining 1/4 teaspoon salt, remaining 1/4 teaspoon pepper, vinegar, shallots, Dijon mustard, and tarragon in a small bowl, stirring well with a whisk. Drizzle dressing over potatoes.