Step 1Trim and discard the roots and dark-green parts from each leek. Halve each leek lengthwise and wash well under running water, fanning the layers and making sure to rinse off every hidden bit of sand. Slice the leeks finely crosswise – there should be 8 to 10 cups.
Step 2In a large, heavy saucepan, melt 4 tablespoons butter over medium-low heat – it will be more than you think you need. Stir in the leeks and a pinch or two of salt. After a couple of minutes, stir in the rest of the butter.
Step 3Cover, reduce the heat to low, and cook for about 20 minutes – the leeks will have all but melted. Do not let them brown.
Step 4Stir in the cream, increase the heat to medium and gently simmer, stirring occasionally until thickened.
Step 5Grind pepper over the top and stir again. Serve.