Start with cold water.
This gives the centers time to heat with the outside.
Find a recipe Soft potatoes hand mashed with butter and warm milk. Start in cold water and add the milk gradually for a texture you can control.

Recipe draft · Reviewed editorially, not kitchen tested by us. Prep: about 15 minutes. Cooking: about 35 minutes. Times vary with equipment and ingredient size. Contains milk. Check butter and milk labels for your requirements.
Peel potatoes and cut into roughly 1½ inch (4 cm) chunks. Place in the large pot, cover with cold water by about an inch and salt the water.
Even chunks soften more evenly than mixed sizes.
Bring to a boil, then simmer for about 15 to 20 minutes. Drain when a knife slides easily into the largest chunk.
Firm pieces leave lumps that are difficult to fix later.
Return drained potatoes to the pot over very low heat for about 1 minute, shaking gently, then remove from heat. Warm milk and 3 tablespoons of butter in the small saucepan without boiling.
Let surface steam escape without scorching the dry pot.
Mash the potatoes by hand. Fold in warm milk and butter a little at a time, then add measured salt and white pepper to taste.
Stop once soft and combined. A blender or vigorous mixing can make the starch gluey.
If too stiff, stir in extra warm milk a tablespoon at a time. Transfer to a bowl and top with the remaining tablespoon of butter.
The mash should mound softly rather than pour like soup.
This gives the centers time to heat with the outside.
A hand masher gives a home style texture. Tiny lumps are preferable to overworking the potatoes.
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