Melt butter in heavy skillet. Add shallots and cook over medium heat until brown and tender, about 20 minutes. Stir often and check the heat so they don't burn. When done set them aside and reserve skillet. You are going to heat the milk in it to get all the shallot flavouring possible.

While the shallots are cooking, peel and cut the potatoes into 2-3" chunks. Cover potatoes with cold water by about 1" in a large sauce pan. Bring to a boil and then cook over medium heat until tender, about 15-20 minutes. Drain potatoes and return to the pan. Stir them over medium heat for about a minute to remove excess moisture. Cover and set aside.

Heat milk in the shallot skillet scraping up any brown bits. Mash potatoes, add remaining 4 Tbsps butter. Add hot milk to the potatoes. Stir in the shallots. Salt and pepper to taste.