Put the potatoes in a large pot and cover with water by 1 inch; season with salt. Bring to a simmer over medium heat and cook until the potatoes are tender, about 15 minutes. Drain well.
Return the pot to low heat. Add the butter and half-and-half. Using a ricer or food mill, press the potatoes into the pot. (You can also use a potato masher, though the potatoes will be slightly chunkier.) Season with 2 teaspoons salt and a generous amount of pepper and stir until smooth.