If the cooked chicken isn't already sliced up chop it up into smaller pieces.
Gently heat the oil and sauté your chopped onions. This can be done in your soup maker if you have one with this function. If not you can do this in a separate saucepan. (Sautéeing is optional - you can just throw the onions in as they are if you prefer).
Switch the sauté function off/transfer onions to saucepan.
Add chicken, chopped tarragon, crushed garlic and vegetable stock cube.
Fill the soup maker up to at least the minimum line with hot water (depending on how thin/thick you want it).
Stir to mix all ingredients.
Set soup maker off to smooth.
Once the soup maker is finished stir in the double cream.