Preheat oven to 150°C/300°F. Heat one tablespoon of neutral oil in a large Dutch oven over high heat until just smoking.
Season the lamb shanks generously with salt and pepper and lay them in the pot, being careful not to overcrowd -- you may have to work in batches. Sear on one side until deeply golden brown before flipping and repeating on the other side, about 5 minutes per side. Remove from the pot and set aside on a plate.
Reduce the heat to medium and add the shallots, garlic and anchovies along with a generous pinch of salt. Cook until the shallots begin to soften and the anchovies are mostly dissolved, about 5 minutes, scraping up any browned bits from the bottom of the pot as the shallots release their moisture.
Add the cumin, fennel, coriander and chili flakes. Cook until very fragrant, about 1 minute.
Add the tomato paste and cook until the paste darkens and gets sticky, about 2 minutes longer. Sprinkle the flour over the tomato paste mixture and cook for another 2 minutes or so.
Pour over the vinegar and fish sauce and cook until it is slightly reduced, only about 30 seconds to one minute.
Return the lamb shanks to the pot along with any accumulated juices. Add the carrots, celery, thyme, bay leaves and lemon zest.
Pour over the chicken stock and bring the mixture up to a simmer. Partially cover the pot and transfer to the oven. Cook for about 3 hours or until the lamb is incredibly tender and almost falling off the bone, flipping the lamb shanks over once halfway through.
Remove the pot from the oven. Transfer the lamb shanks to a plate and set aside. Remove the carrots, celery, thyme, bay leaves and lemon zest from the pot and discard.
Put the pot on the stovetop over medium-low heat and allow the sauce to simmer vigorously for 10-15 minutes, just until it reduces enough to thicken slightly. Return the shanks to the pot to coat in the sauce. Portion out and serve.