1. Preheat oven to 375 degrees F.
2. Peel shallots, leaving the root ends intact so they'll hold together. Place on a large sheet of foil; sprinkle 1 tablespoon oil over the top. Seal the packet and bake until the shallots are tender, about 45 minutes. Remove from foil and set aside to cool.
3. Meanwhile, remove the outer leaves from Brussels sprouts and trim the stems. Cut the small sprouts in half and quarter the larger ones. Place the shallots and Brussels sprouts in a roasting pan. Toss with the remaining 1 tablespoon oil and salt.
4. Increase oven temperature to 400 degrees F. Roast, tossing twice during cooking, until the Brussels sprouts are tender and lightly browned, 25 to 35 minutes.