01 - Melt the unsalted butter in a large heavy-bottomed pot or Dutch oven over medium heat. Add the sliced leeks and chopped onion; cook, stirring occasionally, for 5 to 7 minutes until they are softened and translucent but not browned.
02 - Add the minced garlic to the pot and continue to cook for 1 minute more, until fragrant.
03 - Stir in the diced potatoes and pour in the vegetable broth. Bring the mixture to a boil, then reduce the heat to low, cover partially, and simmer for 20 to 25 minutes, or until the potatoes are very tender and easily pierced with a fork.
04 - Remove the pot from the heat. Carefully use an immersion blender to puree the soup directly in the pot until completely smooth. Alternatively, transfer the soup in batches to a regular blender and blend until smooth, returning it to the pot afterward.
05 - Return the pureed soup to low heat. Stir in the whole milk or heavy cream, along with the salt, black pepper, and optional nutmeg. Heat gently until the soup is warmed through, ensuring it does not come to a boil.
06 - Taste and adjust the seasoning as needed. Ladle the creamy leek soup into individual bowls and garnish with chopped fresh chives or parsley, if desired, before serving hot.