Peel potatoes. You can leave potatoes whole if they are all about the same size or cut the potatoes into quarters or cubes to speed up cooking time, making sure all are relatively the same size. Place in a large saucepan, add the 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 until tender when poked with a fork.
Heat the half-and-half and the garlic in a medium saucepan over medium heat until simmering. Remove from heat and set aside.
Remove the potatoes from the heat and drain off the water. Mash and add the garlic-cream mixture and Parmesan; stir to combine. Let stand for 5 minutes so that mixture thickens and then serve.