Prep the Leeks: Cut the dark green tops off the leeks. Then cut the root end off the stocks as well. Quarter the stocks, lengthwise, and cut into ½-inch slices. Place the chopped leeks in a bowl and rinse thoroughly with cold water to remove any sand and debris. (You can save the green tops for making stock, but do not use them in this recipe.)Move the leeks to a colander to drain while you mince the garlic.
Set a large 6-8 quart soup pot over medium heat. Add the butter, chopped leeks, and garlic to the pot. Stir and allow the aromatics to sauté and soften for 5-10 minutes.
Meanwhile, quarter the potatoes, lengthwise. Then slice into thin slices. Once the leeks are very soft and fragrant, add the sliced potatoes to the pot. Pour in the broth, then stir in the Italian herb seasoning.
Cover the pot and simmer for 20 minutes, stirring on occasion. Then uncover the pot and continue to simmer for another 10 minutes until the potatoes are very soft, and disintegrating into the soup base.
Taste, then salt and pepper as desired. For extra creamy soup, stir in ¼ cup of heavy cream or cashew cream.
