Melt the butter in a large pot over medium heat.

Add the sliced leeks and sauté until soft, about 8 minutes.

Stir in the garlic and cook for 1 minute.

Add the diced potatoes, broth, salt, and pepper. Bring to a boil, then reduce heat, cover, and simmer for 20 minutes until potatoes are tender.

Remove the pot from the heat and use an immersion blender to puree the soup until smooth.

Stir in the heavy cream and fresh parsley. Serve hot.