Preheat the oven to 475 degrees.
Cut the carrots into 2 to 3-inch pieces and then cut the small ends in half and quarter the larger end pieces. Spread them out onto a sheet pan. Toss the carrots with 2 tablespoons of olive oil and season with salt and pepper. Roast for 15 minutes, tossing them once or twice, until the carrots are tender and brown along the edges. Remove from the pan and put into a serving dish.
Combine the dressing ingredients in a jar and shake to combine. Taste and correct seasoning if necessary. Pour the vinaigrette over the carrots; toss slightly and serve.
Best served warm or at room temperature.