Peel and finely dice the carrots and onions. Slice the celery thinly, cutting any larger slices in half or smaller so they are similar size to the carrots and onions.
Preheat oven to 350F/175C.
Warm 1tbsp of the oil in an ovenproof dish large enough to hold both lamb shanks but relatively tightly, so the sauce will come well up the side without needing too much. Add the lamb shanks and brown on all sides, over a medium-high heat - I know this can be tricky given their shape but do as best you can. Remove from pan and set aside.
Add the carrot, onion and celery to the pan along with the rest of the oil and cook, stirring now and then, for a couple minutes until the onions are softened. Reduce heat if needed so they don't burn.
Add the red wine and allow it to bubble a minute then add the tomatoes, stock, tomato paste, mixed herbs, thyme and bay leaf. Stir to ensure mixed then add back the lamb shanks, pushing them under the sauce so they are largely covered.
Cover the dish and transfer to the oven. Cook for approximately 2 hours, a little more is fine, checking after around 1 ½ hours and turning the lamb shanks if they are out of the sauce. If the sauce looks particularly low, add a little more stock but you do want it to reduce a bit (see photos above).
Great served with something to mop up the sauce eg couscous, rice, quinoa or mash.