Peel and dice potatoes. Place potatoes in a large sauce pan, add salt and cover with water. Bring to a boil over medium-high heat and cook until potatoes fall apart when poked with a fork (around 20 minutes). In a medium saucepan, heat milk and garlic over medium heat until simmering. Set aside.
Remove the potatoes from heat and drain the water. Mash the potatoes and add the garlic-milk mixture and whip together using an electric mixer or whisk. Add Parmesan and stir to combine. Let stand for a few minutes to thicken, then serve.