Place the potatoes in a large pot and fill pot three-fourths full with water. Bring to a boil and add the tablespoon of salt. Boil gently until potatoes are very tender and can be pierced easily with a fork, about 15-20 minutes. Drain well in a colander.

In the meantime, warm the half-and-half with the butter in a small saucepan.

If you are serving the mashed potatoes immediately, place a ricer or food mill over a large serving bowl. If you are holding the potatoes for up to 90 minutes before serving, place the ricer or mill over the top pan of a double boiler, or a large heatproof bowl placed over a saucepan of hot water (but not touching the water). Put the potato cubes through the ricer or mill. (Alternatively, mash the potatoes using a potato masher). Slowly add the half-and-half/butter mixture, a little at a time, stirring constantly with a large spoon or a large whisk, until the potatoes are very creamy but not soupy. Season to taste with salt.