When a potato cooks, the starches contained in each cell are released as the cell walls break down. These starches absorb the potato’s internal moisture and swell and soften. These two processes are what transform a raw, hard potato into a cooked, softer potato fit for mashing.
If you cut your potatoes up before boiling them, the starches absorb the internal potato moisture as well as the water in which they’re being boiled. If they boil for too long, they absorb too much water and your mashed potatoes will become gummy. The difference between perfectly cooked potato pieces and soggy pieces can sometimes be as little as a minute or two.
An easy workaround is to boil potatoes whole. They’ll take a bit longer to cook but you can leave them in the hot water after boiling without undesirable effects, keeping them warm until it’s time to mash them. I start my potatoes boiling as soon as I begin cooking and mash them immediately before dinner.
If they need more moisture, you can add a bit of hot potato boiling water or another liquid. This way, you have more control of their moisture content.
I bake my potatoes. Score the skin as shallow as you can into 1" squares or smaller, rub with clarified butter and salt generously. Cook at 400F to an internal temp of about 205F, let cool a bit before mashing. The skin bits will be crisp and delicious.
You have to add a little more liquid back, so have some heavy cream on hand or at least evaporated milk or half-and-half.