Toss the carrots with some olive oil, salt and pepper and bake it at 400 F for about 20 minutes. Make sure that you don't crowd the baking pan and keep them in a single layer.
Layer the sliced nectarine in another baking pan, sprinkle some salt on top and drizzle with some olive oil. Bake it at 400F for about 10 minutes.
For the dressing, combine everything in a glass bowl and let it rest for 15 to 20 minutes to let the flavor meld.
Arrange the greens, roasted vegetables and the grapes in a serving bowl.
Whisk the dressing properly and pour it on the salad just before serving.
Serve it warm at room temperature.