Put the potatoes and peeled garlic in a large pot, cover with cold water by about 1 inch, and add 2 teaspoons kosher salt. Bring the pot to a boil, then reduce the heat to maintain a steady simmer.

Cook the potatoes and garlic for 15–20 minutes, or until the potatoes are completely tender when pierced with a fork. While they cook, warm the butter and heavy cream or whole milk together in a saucepan over low heat, then stir in the thyme without allowing the mixture to boil.

Drain the potatoes and garlic thoroughly, then return them to the hot pot for 1–2 minutes over low heat. This brief drying step removes excess moisture and helps prevent watery mashed potatoes.

Press the potatoes and garlic through a potato ricer or food mill, or mash them by hand for a more rustic texture. Gradually fold in the warm butter-and-cream mixture, followed by the sour cream if using.

Stir in the parsley, chives, black pepper, and additional salt to taste. Serve immediately, topping with the remaining butter if desired.