Melt the butter in a large stockpot over medium heat. Add the onion, celery, and leeks and sweat for 10 minutes, until tender.
Add the tomatoes, bay leaves, salt, pepper, and cayenne and stir to coat the vegetables.
Add the lentils, tomatoes, and stock and bring the mixture to a boil. Reduce heat, partially cover, and simmer for 45 minutes, until the lentils are tender.
Meanwhile, combine the heavy cream and garlic cloves in a medium saucepan. Simmer for 20 minutes, until the garlic is tender and the cream is reduced by half. Remove the garlic cream from the heat and puree in a food processor or blender until smooth, set aside.
When the lentils are tender, stir in the pureed garlic cream. Simmer for 1 minute to heat through.
To serve, remove the bay leaves, ladle the soup into bowls, and top with the chopped chives.