Boil the potatoes: Place peeled, cubed potatoes in a large pot. Cover with cold water by 1–2 inches and add 1 tablespoon of salt. Bring to a boil over high heat, then reduce to a simmer. Cook for 15–20 minutes, or until potatoes are fork-tender and easily break apart.
Drain and dry: Drain potatoes thoroughly in a colander. Return them to the hot pot over low heat for 1–2 minutes, stirring gently to evaporate excess moisture.
Mash the potatoes: Using a potato ricer, food mill, or hand masher, mash the potatoes until smooth. Avoid blenders or food processors, which can make the mash gluey.
Warm the dairy: In a small saucepan, combine butter and milk (or cream). Warm over low heat until butter melts. Do not boil. If using garlic, sauté½½ it in the butter before adding milk.
Combine: Gradually add the warm dairy mixture to the mashed potatoes, stirring with a wooden spoon or spatula. Start with 3/4 cup of dairy and add more as needed for your preferred consistency.
Season: Add 1–2 teaspoons of salt and freshly ground black pepper to taste. If using sour cream or cream cheese, stir in now. Mix gently until smooth and creamy.
Serve: Transfer to a serving bowl and serve immediately. Garnish with extra butter, chives, or black pepper if desired.