Add a drop of olive oil (or butter) to a sauté pan over med/high heat. After it melts, add the onions then the mushrooms and thyme. Saute for approx. 5 minutes or until most of the liquid from the mushrooms has been released.
Transfer the mushrooms and onions to a food processor (removing as many as you’d like if you prefer mushroom pieces in your soup). Pulse to a desired consistency. Pulse a lot for a smoother soup or just a few times for a chunkier soup.
Keep the mixture in the food processor and add the remaining 4 Tablespoons butter to the pan and after it melts add the flour. Whisk the flour for 1-2 minutes to burn off any raw flour taste.
Add the half and half then the chicken stock. Heat until almost boiling, then the sherry. Season with salt and pepper.
Return the mushrooms to the pan, including the pieces that were set aside.
Continue to cook on low until the soup has thickened.