In a large pot, melt the butter over medium heat.
Add the sliced leeks and sauté until they become soft and translucent, about 5-7 minutes.
Stir in the minced garlic and cook for an additional 1-2 minutes until fragrant.
Toss in the bay leaves, thyme sprigs, and diced red potatoes, stirring to combine everything well.
Pour in the concentrated chicken broth (or vegetable broth) and water. Bring the mixture to a boil.
Reduce the heat to medium-low, cover the pot, and let the soup simmer for about 20-25 minutes, or until the potatoes are tender.
Remove and discard the bay leaves and thyme sprigs from the pot.
Using an immersion blender or a regular blender, carefully blend the soup until smooth and creamy. Note: If using a regular blender, blend the soup in batches and be cautious with blending hot liquids to prevent splattering. Allow the soup to cool slightly before blending if using a regular blender. Return the blended soup to the pot, if necessary, and place it over low heat.
Stir in the heavy cream, cayenne pepper, salt, and black pepper, adjusting the seasonings to your taste preferences.
Allow the soup to warm through, but avoid boiling it once the cream is added.
Serve the soup hot, garnished with finely chopped fresh chives if desired.