Season meat: Place the lamb shanks in a large container, sprinkle them with about ½ to 1 tablespoon flour, salt, and pepper, and rub them to coat. Pat gently to remove the excess flour.
Brown lamb shanks: Heat 2 tablespoons of the oil in a large pan. Brown the meat on all sides; it will take about 10 minutes. Turn them often to make sure that all the sides are nicely colored.
Chop the vegetables while the meat browns. Finely chop the onion and the garlic. Peel and cut the carrots at an angle into relatively larger pieces, and cut the celery sticks into small pieces.
Transfer the meat to the slow cooker.
Brown vegetables: Add another tablespoon of oil to the pan. Brown the vegetables for about 3 minutes, stirring often. Add tomato paste and about ½ tablespoon flour (you can use the leftover flour from flouring the shanks). Stir well.
Add liquids: Pour in the red wine and stir well for about one minute. Add the stock, fine sea salt, black pepper, rosemary, thyme, and bay leaves.
Pour the liquid into the slow cooker over the meat.
Cook on high for 4 hours or on low for 8 hours.
Check: Make sure that meat is tender. Check with a fork; you should be able to pull the meat off the bone easily. If they are not quite there yet, give them another 30 minutes, then check again until they are as tender as possible.
Remove the meat pieces from the crockpot with a slotted spoon. Keep warm until you make the sauce.
Pour the contents of the slow cooker into a large pan.
Whisk the cornstarch with a bit of cold water in a small bowl until you have a thick yet pourable paste.
Thicken sauce: Once the sauce starts to boil gently, start whisking in the cornstarch mixture. Stir well and let bubble gently until the sauce thickens to the desired consistency; it should take 2-4 minutes.
Adjust the taste with salt, pepper, balsamic vinegar, and sugar (if necessary, see Note 3).