Peel and dice potatoes, 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 fall apart 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.