Season the shanks liberally with salt and sear them with a little veg oil in a large pot on high heat. Once the shanks are browned on both sides, add enough cold water to cover. Add the halved head of garlic, celery, carrot, bay leaves, thyme sprigs and peppercorns. Cover and bring to a boil. Turn the heat down to medium and simmer for 2 1/2 hours. Skim any pooled fat and gunk from the surface occasionally.

Remove the shanks and set them aside to cool. Strain the braising liquid thorough a sieve lined with a coffee filter.

Add the butter to a medium pot on medium-high heat. Add the onion and sliced carrots and fry 2 minutes. Add the tomato paste and chopped garlic and continue cooking another 2 minutes. Deglaze the pot with the sherry and let simmer until about 3/4 of the sherry has boiled off.

Strip the meat and any marrow off the shanks and add it to the pot along with the strained braising liquid, beef stock, potatoes, rosemary and thyme. Let simmer for 30 minutes. Add the beans and capers and simmer for 5 minutes more.

Make a slurry by adding a splash of water to a bowl and adding the cornstarch. Whisk until smooth. Whisk the slurry into the pot and let the stew simmer for a final 5 minutes. Add any extra salt and pepper as needed before serving.