Step 1

Put the potatoes in a large pot and cover with 1 inch of cold water. Add a lot of salt, about 2 1/2 tablespoons — taste it, and it should taste almost too salty for another sip. Bring to a boil over high, then reduce heat and simmer until potatoes are fork-tender, 10 to 20 minutes, depending on the size of the potatoes.

Step 2

Meanwhile, remove the two outer layers of the leeks, slice lengthwise and rinse to clean out any grit, then thinly slice the white and light green parts crosswise (save the dark green parts for stock). Coarsely crush the peppercorns with the bottom of a mug or a meat mallet.

Step 3

Drain the potatoes into a colander and leave in the sink to drain further. Wipe out the pot; no need to wash it. Add the butter to the pot and set over medium heat. Once it's melted, add the leeks, season with salt to taste, and cook until they're softened (the color should be bright green), 5 to 7 minutes. Add the peppercorns, stir to coat, then turn off the heat.

Step 4

Using your hands, the bottom of a mug or a meat mallet, lightly crush the potatoes so the skin splits in spots. Add the potatoes to the pot as you crush them, then stir gently to coat them in the leek butter. Season to taste with salt, and serve right away.