Add the minced garlic and cook for 1 minute until fragrant.
Pour in the broth. Add the diced potatoes, salt, and pepper. Bring the mixture to a boil, then reduce heat, cover, and simmer for 15 to 20 minutes, or until the potatoes are very tender.
Remove the pot from the heat. Use an immersion blender to blend the soup until completely smooth and creamy. Alternatively, carefully transfer the soup in batches to a standard blender and blend until smooth, then return it to the pot.
Stir in the heavy cream (or coconut milk). Heat gently over low heat until warmed through. Do not boil after adding the cream.
Taste and adjust seasoning if needed. Ladle the soup into bowls and garnish with fresh chives before serving.
Notes
To clean leeks, slice them lengthwise, then rinse them thoroughly under cold running water in a colander to remove trapped dirt.
For a richer flavor, roast the garlic before adding it to the pot.
If you prefer a thinner soup, add more broth until you reach your desired consistency.