Cut the ends off the shallots and peel them. If you are struggling with getting the skin off, make a shallow cut along the length of the shallot and then peel. Place them on a small baking sheet and drizzle them lightly with olive oil.
Pour on the balsamic vinegar and sprinkle with a good pinch of salt and a few grinds of pepper. Use a rubber spatula or your hands to mix well.
Lay down the thyme sprigs and cover the pan with foil. Bake for 20 minutes, then remove the foil and bake for another 15 minutes. Remove and discard the thyme sprigs. Allow to cool slightly and serve.