Add peeled, cubed potatoes to a large pot and cover with cold water. Salt the water generously.
Bring to a gentle simmer and cook until potatoes are completely tender.
Drain well and return potatoes to the warm pot. Let steam evaporate 2–3 minutes.
Mash the potatoes while hot.
Warm the milk and butter together in a small pot or microwave until melted and steamy.
Pour the warm milk-butter mixture into the potatoes a little at a time while mashing until smooth and creamy.
Season generously with salt and coarse black pepper. Taste and adjust until perfect.