Prepare leeks and garlic: In a large soup pot, melt 3 tablespoons of unsalted butter over medium heat. Add the chopped leeks and smashed garlic cloves, cooking gently for about 10 minutes, stirring regularly. Make sure the leeks soften without browning.
Add potatoes and seasoning: Add the 2 pounds of diced potatoes, 7 cups of chicken or vegetable broth, 2 bay leaves, 3 thyme sprigs, 1 teaspoon salt, and ¼ teaspoon black pepper. Bring the mixture to a boil, then cover and lower the heat to a simmer. Cook for 15 minutes, or until the potatoes are very tender.
Blend and season: Remove the bay leaves and thyme sprigs. Use an immersion blender to purée the soup until smooth. (Alternatively, transfer the soup in batches to a regular blender, blending until smooth.) Stir in 1 cup of heavy cream, bringing the soup to a gentle simmer.
Adjust consistency: If the soup is too thick, add a little water or stock. If it’s too thin, let it simmer a bit longer to thicken.
Serve: Ladle the soup into bowls, garnishing with finely chopped chives for a fresh flavor boost.
Enjoy this classic, warming soup!