Trim and slice leeks (discard dark green tops), then rinse well to remove dirt.
Peel and dice potatoes into 1-inch cubes.
Heat butter/oil in a large pot over medium heat.
Add leeks and sauté for 5 minutes until softened.
Stir in garlic and cook for 1 minute until fragrant.
Add potatoes, broth, water, bay leaf, thyme, salt, and pepper.
Bring to a boil, then reduce heat and simmer for 20 minutes until potatoes are tender.
Remove the bay leaf, then use an immersion blender to puree until smooth (or blend in batches in a regular blender).
Stir in heavy cream and simmer for 2–3 minutes. Adjust seasoning if needed.
Ladle into bowls and garnish with fresh chives, black pepper, or crispy bacon.