Peel the potatoes and cut them into 2.5cm (1in) slices. Run the slices under cold water to wash off surface starch. Heat a large pan of water until it reaches a temperature of 80C/175F (you'll need to use a good-quality heat thermometer, with the probe placed in the water. Add the potatoes and simmer for half an hour being careful to maintain the temperature at 70C/160F. Drain the potato slices and run them under cold water until completely cool.
Rinse the pan and refill with cold water. Salt the water and bring it to the boil, then lower to a simmer. Add the cooked, cooled potatoes and cook until soft. Drain the potatoes, then place them back in the pan. Shake the pan over a gentle heat to get rid of any remaining water.
Tip the potatoes into a ricer and rice the potatoes over a bowl containing the cold butter. Push the buttery riced potatoes through a fine-meshed drum sieve for a silky, light texture. You can prepare the purée in advance up to this stage and store it in the fridge. To serve, reheat it gently in a pan, while gradually whisking in a little warm milk.