Prep the potatoes: Place potato chunks in a large pot and cover with cold water by about 1 inch. Stir in 1 tablespoon kosher salt.
Bring to a gentle boil, then simmer until fork-tender, 12–15 minutes.
Infuse the dairy: While potatoes cook, add milk, butter, smashed garlic, and thyme to a small saucepan. Warm over low heat until butter melts and small bubbles appear at the edges. Remove from heat and let steep.
Drain and steam-dry: Drain potatoes well and return to the hot pot.
Set over low heat for 1–2 minutes, stirring occasionally, to evaporate excess moisture.
Mash: Remove garlic cloves from the milk mixture. Mash potatoes with a potato masher or ricer. Slowly pour in the warm infused milk-butter, mixing gently until smooth and fluffy.
Finish the flavor: Fold in sour cream, parsley, chives, pepper, and Parmesan if using.
Taste and adjust salt. The texture should be creamy but hold soft peaks.
Make ahead: Transfer to a buttered baking dish. Dot the top with a few small pieces of butter.
Cool, then cover tightly and refrigerate up to 2 days.
Reheat to serve: Bake covered at 350°F (175°C) for 25–35 minutes until hot, stirring once and adding a splash of milk if needed. Finish uncovered for 5 minutes for a lightly golden top.