Put a small amount of fat into your pot.(duck is best, but others will do) Heat this up & then put the shanks in and brown turning frequently.
Meanwhile be chopping up the Onion, carrot, celery mixture.(How finely you chop depends upon how you plan to finish the dish.More on this later).
Peel & roughly chop the garlic.
When the shanks are nicely browned remove them from the pot & set aside.Put the vegetable mixture along with the garlic & bay leaves into the pot, turn down the heat to low, cover the pot & sweat the mixture for at least 20 minutes.
Rub your rosemary & thyme as you strip the leaves from the stalks.
Put the lamb shanks back into the pot with the sweated veggies.Add the herbs.Add the wine & stock to just cover.(I like to use about 50% wine, 50% stock.) Give everything a light seasoning.
Bring to the boil then back down to a simmer.Cover & simmer slowly for at least 3 hours.Check & stir occasionally.
At the end of this first cooking take the shanks out & put them in the fridge separately from the vegetables & sauce.
Next day bring everything back up to room temperature having skimmed off any fat from the sauce.(there normaly woN°t be much if any.) Now its decision time.How to finish the dish as there are lots of variations.
A) my favorite 'classic' version.for this one I would have chopped the veggies much more finely.I would now add some crushed juniper berries and about 3 oz of tomato puree.Everything back into the pot for at least 2 hours covered.Shanks out.Veggies & stock through a strainer or food mill then back into the pot for a final reduction.Add some butter just before serving to give a nice finish.Serve over potatoes, rice or other root vegetables.
B) An Italian, "osso bucco" slant.As in A, but no juniper.Add oregano & fennel seeds, the tomato puree & a can of italian plum tomatoes, drained.Cook as before except stir more often to crush the plum tomatoes.Serve over pasta, polenta or rice.
C) The 'stew' version.This is the one I've shown with roughly chopped veggies.I now, for the second cooking, add green lentils (about 4 oz per person) or white beans which have been soaked & pre-cooked.Everything together & cook for closer to 3 hours than 2.Serve as is.There are about as many variations upon this basic recipe as there are cooks.