Prepare the Leeks: Trim, clean, and slice the leeks. Leeks can trap dirt, so rinse carefully.
Sauté the Leeks: In a large pot, melt butter over medium heat. Add leeks and sauté 5–7 minutes until softened but not browned.
Add Potatoes and Broth: Add diced potatoes, broth, bay leaf, salt, and pepper. Bring to a boil.
Simmer: Reduce heat, cover, and simmer for 20–25 minutes until potatoes are tender.
Remove Bay Leaf: Discard the bay leaf.
Blend the Soup: Use an immersion blender to puree until smooth, or transfer in batches to a blender.
Adjust Consistency: Add water or more broth if needed. Stir in heavy cream, if using, for extra richness.
Season: Taste and adjust salt and pepper.
Garnish: Serve hot, garnished with fresh chopped chives.