Preheat the slow cooker on the HIGH setting.
Peel the carrot and onion, wash the celery, and trim the ends.
Chop the vegetables into small pieces.
Heat the oil in a frying pan and cook the vegetables over a low to medium heat for 5 minutes, stirring occasionally.
Transfer the vegetables to the slow cooker with a slotted spoon.
Pat the turkey dry with kitchen paper and season the breast.
Add the butter to the pan over a medium heat and brown the turkey breast for a few minutes,
Put the turkey on top of the vegetables in the slow cooker.
Add the stock and tarragon to the pan and bring to the boil. Use a wooden spoon to loosen any bits stuck to the pan.
Pour the hot stock around the turkey.
Cook the turkey for 4 hours, or until the juices run clear.
Let the turkey rest for 20 minutes on a plate, covered loosely in foil.
Skim off any fat from the surface of the mirepoix stock, then transfer the liquid to a blender and process until smooth.
Transfer the gravy to a saucepan and season to taste.
Warm the gravy over a medium heat to serve.