Peel and dice the potatoes, then place them in a large pot with the peeled garlic cloves.
Add enough water to cover the potatoes, then mix in the salt and rosemary sprigs.
Bring to a boil over medium high heat, then reduce to medium heat, cover, and cook for 15–20 minutes or until fork tender.
Strain off the water and remove the rosemary sprigs. Add the butter and let it melt into the hot potatoes.
Mash using a potato masher, immersion blender, or potato ricer until smooth. Add a splash of heavy cream, olive oil, or sour cream if desired.
Taste and adjust seasoning. Serve warm with a drizzle of melted butter or a few sprigs of rosemary for garnish.