Heat the butter and flour in a dutch oven over medium heat, stirring continuously to make a light brown roux (3-5 minutes).
Add the onion, garlic and green pepper and cook for about 2-3 minutes, until vegetables start to soften.
Then add the tomato paste and sherry and cook for 1-2 minutes. The mixture will be thick.
Add the Cajun seasoning, tarragon and seafood/fish stock slowly, stirring while adding a little at a time to ensure the roux doesn't get lumpy. Bring to a boil over high heat, then reduce the heat and simmer for 10 minutes over medium heat.
Use an immersion blender to blend the soup. Blend for 3-5 minutes, or until the soup is creamy. **If you don't have an immersion blender, remove the soup from the heat and blend in batches. Place blended soup back in the dutch oven and heat to a simmer.
Add the crawfish tails and cream and simmer for 5 minutes. Reserve a couple crawfish tails for serving if desired. Serve in bowls garnished with croutons, green onions and reserved crawfish tails.
When cooking the flour and butter to make a roux, make sure to stir constantly to prevent it from burning. It is done when it is a very light brown/cream color. It should take 3-5 minutes.
Make sure to add the WARMED seafood stock slowly to the mixture while stirring. This helps prevent lumps from forming.
When using the immersion blender, blend for 3-5 minutes, or until the soup is creamy. It's ok if there are a few small chunky pieces.
If using a stand blender instead of an immersion blender, make sure to let the liquid cool slightly before blending; otherwise the heat can make the lid explode off causing a huge mess.