Peel the potatoes. Cut the potatoes in half, and then quarter the half slices. Place in a large saucepan, add salt, and cover with water. Bring to a boil over medium-high heat and then reduce heat to maintain a rolling boil. Cook until potatoes are fork-tender.
Melt butter in a small saucepan and add garlic when lightly foaming. Saute until garlic is fragrant (be sure not to brown!).
Remove the potatoes from the heat and drain off the water. Mash with a potato ricer, or mixer. Add butter-garlic mixture and half-and-half; stir to combine. Let stand for 5 minutes until it thickens and serve.