1In a Dutch oven or heavy pot over medium heat, melt the butter (or warm the oil). Cook the leeks with a sprinkle of salt until tender, about 5 minutes.
2Add the potatoes, broth, and 1 teaspoon salt; stir to mix well. Bring to a boil, partially cover, reduce the heat to low, and simmer until the potatoes are tender, about 20 minutes.
3Depending on how smooth or chunky you like your soup, you can purée it in a blender (very smooth), puree it with an immersion blender (smooth), or use a potato masher to mash the potatoes until slightly chunky.
4Taste and adjust the seasoning with salt and pepper. Serve in warmed bowls.