In a large Dutch oven or heavy-bottomed pot, melt the butter over medium heat. Add the cleaned and sliced leeks and cook, stirring occasionally, for about 8-10 minutes until they are very soft and wilted but not browned. Add the minced garlic and cook for another minute until fragrant.

Add the peeled and cubed potatoes, broth, bay leaf, and thyme sprigs to the pot. Season with salt and pepper. Bring the mixture to a boil, then reduce the heat to a simmer.

Let the soup simmer for 15-20 minutes, or until the potatoes are fork-tender.

Remove the pot from the heat and discard the bay leaf and thyme sprigs. Use an immersion blender to blend the soup directly in the pot until it's completely smooth. Alternatively, carefully transfer the soup in batches to a regular blender.

Stir in the heavy cream (if using) until well combined. Taste and adjust seasoning with more salt and pepper if needed. Serve hot, garnished with fresh chives.