Cook garlic slowly with 4 tablespoons butter in a 3- to 4-cup covered saucepan until very tender but not browned, about 20 minutes.

Whisk in the flour and cook over low heat until it froths with the butter for 2 minutes without browning. Remove from heat and whisk in the boiling milk, salt, and pepper. Return to heat and boil for 1 minute, stirring.

Press the sauce through a sieve using a spatula, or puree it in a blender until smooth. (Tip: Sauce may be made ahead of time. Dot with butter to prevent a skin from forming and reheat when needed.)

While garlic cooks, bring a large pot of salted water to a boil over high. Add potatoes and cook until tender, about 18 minutes. Drain immediately. Press potatoes through a ricer back into the large pot.

Heat the pot over medium and stir the riced potatoes with a spatula for 1 minute to evaporate any excess moisture. As soon as the puree begins to form a film at the bottom of the pot, remove from heat and fold in the remaining 4 tablespoons butter, 1 tablespoon at a time. Season with salt and white pepper. (Tip: If not serving immediately, leave uncovered. To reheat, cover and set over boiling water, stirring frequently.)

Shortly before serving, stir the hot garlic sauce vigorously into the hot potatoes. Beat in the cream by spoonfuls but do not thin out the puree too much. Fold in the parsley and add additional salt and pepper, if desired. Serve hot.