Prepare the leek by slicing off the dark green top and the root end, then slicing the leek in half lengthwise. Cut each half into slices about ¼ inch thick.
Add the sliced leeks to a bowl of water, and gently agitate them with your fingers to dislodge any dirt. Scoop the leeks out of the water using a slotted spoon.
Melt the butter in a large pot over medium heat. Add the leeks and garlic to the pot, and cook, stirring frequently, until the leeks are softened.
Add the flour and stir to make a paste. Cook for 2-3 minutes, until golden. Whisk the milk into the pot and cook until slightly thickened. Add the chicken broth, potatoes, salt, and pepper, and bring the soup to a simmer.
Simmer for 20-30 minutes, or until the potatoes are tender and the soup is thick.
Serve hot with shredded cheese and crumbled bacon on top, if desired.