Peel potatoes, cut into 1½" chunks, rinse and place in large saucepan. Fill saucepan with enough water to cover potatoes by 1". Heat potatoes over high heat until boiling then reduce heat to simmer, add 1 tsp kosher salt and stir. Simmer until potatoes are very tender but not disintegrating (about 20 minutes). Drain potatoes completely and return to pot.

Stir potatoes over low heat to allow excess water to evaporate—potatoes should break down easily just from stirring (the process is complete when steam no longer rises from the pot—approximately 1 minute).

Transfer potatoes to large mixing bowl or to bowl of stand mixer fitted with whip attachment. Begin beating potatoes on low speed, gradually working up to medium speed to break down any lumps. Add butter, beat on medium speed until fully incorporated, scraping sides of bowl often. Add half-and-half or milk and beat on medium speed until potatoes are light and fluffy.

Sprinkle surface of potatoes with salt and whip on high speed an additional 20 seconds.

Test for seasoning, transfer to serving dish and enjoy!