If you top & tail and remove the outer layer, as said, then keep the bottom white root whole, cut from the middle of the leek towards the top green leaves, once from 12 to 6 and once from 9 to 3 (looking down on said leek) you should have opened out the top to enable you to easily rinse off any mud. It's much easier done than explained!
We often make a simple leek and potato soup, soften a little onion for several long minutes, add chopped leak and cook until soft, add diced potato and cook for a little before adding water/stock, herbs and black pepper to taste. Simmer until the potato is cooked.