Place potatoes and garlic in a large heavy saucepan. Add water to cover and season with salt. Bring to a boil. Reduce heat to medium, cover, and cook until potatoes are very tender, 10 to 15 minutes.
Meanwhile, melt butter in a small saucepan over low heat and cook, swirling, until it turns a nutty brown, about 1 minute. Stir in buttermilk and heat until just warm. (Do not overheat or it will curdle.)
When potatoes are done, drain in a colander and return to the pan. Place pan over low heat and shake for about 1 minute to dry potatoes.
Mash the potatoes and garlic with a potato masher, an electric hand-held mixer or by working through a ricer. Add enough of the buttermilk mixture to make a smooth puree. Season with salt and pepper and serve.
Though the exact health benefits of garlic are controversial, there's no doubt that it contains potent disease-fighting phytochemicals.