In a large pot, melt the butter over medium heat. Add the chopped leeks and garlic, cooking gently while stirring frequently, until they become tender and translucent, about 10 minutes. Adjust the heat as needed to prevent browning.

Introduce the diced potatoes, broth, bay leaves, thyme sprigs, salt, and pepper into the pot. Increase the heat to bring the mixture to a boil, then reduce it to a low simmer. Cover and cook for approximately 15 minutes, or until the potatoes are completely softened.

Remove and discard the thyme sprigs and bay leaves. Use an immersion blender to purée the soup directly in the pot until velvety smooth. If a standard blender is preferred, purée the soup in small batches, ensuring the blender is not overfilled (refer to note for safety).

Stir in the heavy cream and gently heat the soup to a simmer. Taste and adjust the seasoning with additional salt or pepper if necessary. For a thicker consistency, simmer the soup uncovered until it reduces slightly. If it seems too thick, incorporate additional water or broth to achieve the desired texture.

Ladle the soup into bowls and garnish with a sprinkling of freshly chopped chives before serving.

Note: When using a traditional blender, only fill the container halfway, leaving the lid vented to release steam, and cover with a towel to avoid splatters. Transfer the blended soup into a clean pot for reheating.

Freezer-Friendly Tip: To freeze, omit the cream and store the soup in an airtight container for up to three months. Thaw in the refrigerator for 12 hours, then reheat on the stovetop over medium heat until thoroughly warmed. Stir in the cream during reheating and bring the soup to a gentle simmer before serving.