In a bowl toss together the potatoes, quartered, the shallots, 4 tablespoons of the oil, the bay leaf, the dried thyme, the garlic, and salt and pepper, to taste. Spread the vegetables in an oiled large roasting pan and roast them in the middle of a preheated 375 degree F oven, shaking the pan every 5 to 10 minutes, for 25 minutes.
In a bowl toss the squash with the remaining 1 tablespoon oil and salt and pepper to taste and add it to the pan. Roast the vegetables, shaking the pan occasionally, for 10 to 20 minutes more, or until they are tender. Discard the bay leaf and garnish the vegetables with the thyme sprigs.