Place potatoes in a large saucepan, and add enough water to cover by at least 2 inches. Add salt. Bring to a boil; reduce heat and simmer until potatoes are fork tender, about 15 minutes. Drain, and return to saucepan. Stir until dry.
Pass potatoes and garlic through a ricer into a large bowl; Stir until smooth.
Return potato mixture to saucepan. Add heavy cream and butter; stir to combine. Keep warm until ready to serve.
Place saucepan over low heat and stir in cheese curds until melted, adding milk to thin, if necessary; serve immediately.