Put the potatoes, whole, in a pot and cover with cold water. Salt the water. Bring to a boil, and simmer until very tender, about 30 minutes, depending on size.
Meanwhile, drop the garlic, bay leaf, and thyme in a saucepan with the milk, bring to a boil, turn off the heat, cover, and set aside to infuse 10 minutes. Pull out the garlic and herbs, and discard.
When the potatoes are done, drain them and peel while hot. Put them through a food mill set on the smallest setting over a large pot. Beat in the butter a piece at a time. Bring the milk to a boil and beat it in, splash by splash, until completely absorbed. You are looking for a very soft, fine puree, not unlike baby food! Check the seasonings, and serve.