In a large heavy pot, melt butter over medium-low heat.
Add the sliced leeks to the pot. Cook them, stirring occasionally, until they are soft and translucent, roughly about 8 to 10 minutes.
Next, add the minced garlic and cook for another minute, or until fragrant.
While the leeks and garlic are cooking, chop the asparagus into 2-inch pieces.
Once the garlic is ready, add the chopped asparagus to the pot with the leeks and garlic.
Pour in the chicken broth and bring the mixture to a boil.
Once boiling, cover the pot and reduce the heat. Let it cook for about 20 to 25 minutes or until the asparagus is very tender.
After cooking, remove the pot from heat. Using a blender, puree the mixture until smooth.
Once pureed, taste the soup and adjust with kosher salt and fresh pepper to satisfy your palate.
To serve, divide the soup into 5 bowls and garnish each with a teaspoon of creme fraiche and optional chives.