Scrub the potatoes under running water, peel, and remove damaged areas. Cut into evenly sized pieces about 1 1/2 inches across.

Place the pieces in the pot and cover with cold water by about 1 inch. Bring to a gentle boil, then lower the heat to maintain a steady simmer.

Simmer for about 15–20 minutes, checking the largest piece with a fork. It should yield easily all the way to the center. Give firm pieces longer rather than trying to mash them hard.

Drain thoroughly in the colander. Return the potatoes to the warm pot over low heat for about 1 minute, gently moving them as excess moisture steams away. Do not let them brown.

Remove the pot from the heat. Mash by hand until the pieces break down, then fold in the butter. Add the warm milk gradually with the measured salt and pepper, folding only until combined. Stop before the potatoes become sticky; do not use a blender or food processor.

Taste and adjust seasoning, then serve warm. Refrigerate leftovers in shallow covered containers within 2 hours, or within 1 hour above 90°F. Keep at 40°F or below and use within 3–4 days. Reheat to 165°F, stirring gently; add a little warm milk only if needed.