Prepare the Leeks: Slice the leeks into thin rounds, then place them in a bowl of cold water. Swish them around to remove any dirt, then drain and set aside.
Sauté the Leeks: In a large pot, melt butter over medium heat. Add the garlic and sliced leeks. Cook for 5-7 minutes, stirring occasionally, until the leeks become soft and fragrant.
Add Potatoes and Broth: Stir in the diced potatoes and pour in the broth. Bring to a gentle boil, then reduce heat to a simmer. Let it cook uncovered for about 20 minutes or until the potatoes are fork-tender.
Blend the Soup: Use an immersion blender to puree the soup until smooth. If using a standard blender, allow the soup to cool slightly before blending in batches to avoid splattering.
Add Cream (Optional): Stir in the heavy cream for extra richness. Taste and adjust seasoning with more salt and pepper if needed.
Serve & Garnish: Ladle into bowls and top with chopped chives, croutons, or an extra drizzle of cream. Serve with crusty bread for dipping.