Rinse the leek, trim off the top, and cut the roots off the bottom. (Some recipes say to use only the very light green or white parts of the leek, but I hate to waste it so I use it all - which is why my soup looks a bit green). Then cut the leek in half lengthwise, so each outer layer can be penetrated by water. Soak the leek for about 10 minutes and be sure to rinse out all the dirt between layers thoroughly. Then chop it into 1/2 inch slices.
Peel the potatoes and chop them into 1 inch cubes, then set them aside. (You can put them in water so they don't discolor, if you want.)
Place the butter and olive oil in a large, pot over medium heat. Add the leeks and stir until wilted - about 7 to 10 minutes. Then drain the potatoes, and add them and the broth to the pot.
Let the potatoes cook until they are very soft. Then, with a stick blender, blend the mixture until it's creamy. You can put it through a strainer if you want, but I like the occasional little piece of potato. Add the 1/2 cup of whipping cream and return to stove to heat it through.
Serve hot and garnish with some hot crumbled bacon, or sour cream, or crispy fried onions, or whatever you like.