Heat the oil in a large casserole, then brown the lamb shanks well.
Use tongs to take the shanks out of the casserole and put them in a dish to one side.
Add the onions, carrot, celery and garlic into the casserole and cook gently until the finely chopped vegetables are soft.
Add the anchovies and stir to dissolve them into the mixture.
Add the red wine and cook for 3-4 minutes, stirring and scraping to de-glaze the pan.
Put the lamb shanks back in the pan, add stock to cover them, and bring to the boil. Cover with a lid and simmer for 1.5-2 hours until the meat is tender. Check a few times to make sure the shanks are still covered with liquid - if not, top the casserole up with more stock.
While the lamb shanks are cooking, make your pastry. slide the lids over the shank bone to fit on top of the pudding tins, with a 1-1.5cm overhang around the edge.
Put the butter and flour into a food processor and pulse until you have coarse breadcrumbs. Leave a few lumps of butter bigger than others - this will make the pastry slightly flaky.
Add the cream cheese and pulse a few times more, until the pastry starts to come together in a ball.
Tip the pastry out and shape it into a solid ball. Pat it down into circle 3cm thick, then wrap it in cling film and put it in the fridge for 30 minutes.
After 1.5-2 hours, the lamb shanks should be very tender but not yet falling off the bone.
Put one lamb shank upright in each pudding tin, then divide the remaining sauce among the tins - reduce it or top it up with stock accordingly.
Preheat the oven to 200C (180C fan).
Let the shanks cool in their tins for 15 minutes then roll out the pastry, just big enough to cut four lids each 2-3cm bigger than the top of your pudding tins. Cut an X in the middle of each to slide the shank bone through.
Slide the lids over the shank bone to fit on top of the pudding tins, with a 1-1.5cm overhang around the edge.
Pinch the pastry around the edge of the tin to secure it. Cut the pastry in a circle around the bone, so that air can escape.
Beat together the egg and cream, and brush this egg wash on top of the pastry lids. Bake for 25 minutes until golden brown.
Let the pies cool for five minutes before serving them in their tins with mashed potato, mint sauce, and sautéed greens.