In a medium saucepan, toss potatoes and 2 teaspoons salt. Cover with cold water and bring to a boil over high heat. Cook potatoes until fork-tender, 15 to 18 minutes.
Drain potatoes and transfer to a ricer or food mill. Extrude potatoes back into saucepan and cook over medium heat. Add garlic, butter, and wine and cook, stirring frequently, until wine has nearly evaporated and butter is melted, about 2 minutes.
Gradually add cheese and cream, whisking to combine. Continue to cook, stirring, until cheese is melted, 2 to 3 minutes; season with salt.
