Saute the onion, and celery in olive oil and butter over medium high heat until soft.  Add the tarragon, salt, and garlic, and cook for one minute or until fragrant.

Pour in the chicken stock and the broccoli stems.  Bring the mixture to a boil, then reduce to a simmer.  Cook for 10 minutes or until the stems are soft.

Puree the mixture in a blender in 2-cup batches, then return to the pot.  Take care not to burn your hands with the steam or a splatter of hot soup.  As an extra caution, use a tea towel on top of the blender's lid to absorb any spills.

Add the broccoli florets and cook for 5 minutes.

While the broccoli florets are cooking, make the beurre manié by adding the softened butter to the flour in a small bowl.  Mash with a fork until well combined to make a paste.

Remove the soup from the heat.  Whisk in one rounded tablespoon of beurre manié at a time until all the paste is gone and has dissolved in the soup.

Stir in half of the crumbled Silton, then transfer the soup to a serving bowl.  Garnish with freshly cracked black pepper and crumbled Silton.  Serve immediately.