Warning: I tend to like hearty soups. The joke used to be that if a spoon didn't stand straight up in the bowl on its own, then I needed to add noodles.
This soup isn't thick enough to hold a spoon up, but it's definitely not a broth. If you prefer a thinner soup, feel free to add more stock, milk, or water, to thin it to your desired consistency. Then taste for seasoning, because when you water it down, you might find that you need a bit more flavoring.
When you refrigerate the leftovers, they'll thicken considerably, but it will loosen as it warms up.
If you've never worked with leeks before, be warned. They can have grit and dirt between the layers, and much further down that you'd expect. You can cut them in half lengthwise and rinse between the layers, or you can slice them then wash the slices as you would spinach or lettuce, to remove the dirt.
Cheddar Potato Leek Soup
2 pounds potatoes, peeled and cut into chunks
3 leeks, white and tender green, well cleaned and sliced
2 quarts chicken stock
2 tablespoons bacon fat (optional)
2 teaspoons salt (or to taste)
2 cups milk
1/2 teaspoon ground white pepper
8 ounces mild cheddar cheese, shredded or cut into small pieces
Put the potatoes, leeks, chicken stock, and bacon fat (if using) into a heavy-bottomed large saucepan. If the liquid doesn't cover the potatoes, add water, just to cover the potatoes.
If you're using a low-sodium chicken broth, add 1 teaspoon of salt now. Otherwise, wait to season until later. Bring to a boil, then lower to a simmer. Cook, covered, until the potatoes are falling-apart tender.
Add the milk and use a stick blender to puree the mixture. Add the pepper.
Add the cheese, a small hand full at a time, stirring to melt it into the soup. Add more cheese as the previous addition is just about melted.
When all the cheese is added, decide if you like the thickness, and add more liquid, if desired. You can add milk, stock or water.
Taste for seasoning and add more salt or pepper, if desired.