1. Preheat oven to 400 degrees F. Place the shallots, oil, broth, thyme, pepper, and salt in the smallest ovenproof dish you have. Cover with foil and roast until the shallots are very soft and brown (45 minutes). Remove the casserole from the oven.
2. While shallots are roasting, boil the potatoes until soft (30-35 minutes).
3. Drain the water from the pot. Add milk to the potatoes and whip to desired consistency. Stir in roasted shallots mixture.