Remove roots from the leeks and cut in half lengthwise. Rinse well under cold water, then slice into ¼-inch strips on the diagonal.
Add potatoes to a large pot of water so they are fully submerged. Bring to a boil and cook until fork tender. Drain about half the water into a separate bowl; set aside. Add cream to potatoes and mash until fairly smooth. Add leeks and carrots and bring to a simmer. You should have a soupy consistency. If it is too thick, add some of the reserved potato water to liquify. Cook at a low simmer for 15 minutes, stirring occasionally until carrots are tender. Season with a ¼ tsp nutmeg, a good amount of salt and pepper, and serve.