Heat the olive oil in a large Dutch oven or braiser over medium heat. Pat the lamb shanks dry and sprinkle generously with kosher salt. Place the shanks in a single layer in the Dutch oven. Allow the shanks to brown on the bottom before flipping over to another side. Continue cooking the shanks until all sides are browned. Remove the shanks to a plate and set aside.
Turn the heat down to medium low, adding a little more olive oil if the pan is dry. Add the finely chopped onion, celery, and carrots and sauté for 4 to 5 minutes until softened and golden brown.
When the vegetables have softened, add the minced garlic, tomato paste, Worcestershire sauce, brown sugar, kosher salt, and pepper. Sauté for another minute until the garlic is fragrant. Add the stout and beef broth to the pan and bring to a simmer. Return the shanks to the braising liquid. Tie the fresh thyme sprigs and bay leaves together and add to the pan.
Once the braising liquid comes to a boil, reduce the heat to low, cover, and allow to cook at a gentle simmer for 2 1/2 to 3 hours. Skim the liquid occasionally to remove any excess fat and impurities. Flip the shanks 2 or 3 times while braising to ensure even cooking.
Pie Crust
In the bowl of a food processor, combine the flour and kosher salt. Pulse once or twice to mix. Add the diced cold butter and pulse several times until the butter resembles small peas. Pour the ice water into the food processor while pulsing. Continue pulsing until the dough begins to stick together in small clumps. Check the dough – it should stick together if you squeeze it.
Dump the dough mixture onto the counter and use your hands to press it together. Divide the dough in four and shape each piece into a flat disc. Cover with plastic wrap and chill for at least 1 hour.
Finish the Pies
When the lamb shanks are tender and the meat pulls away easily from the bone, remove the shanks to a plate and set aside. Skim any fat from the surface of the braising liquid and taste to adjust the seasoning. Turn the heat up to medium high and bring to a gently boil. Spoon off about 1/3 cup of the braising liquid into a small bowl. Add the flour and whisk until smooth to make a slurry.
Slowly stream the slurry into the boiling liquid, whisking constantly to prevent lumps. Cook for another 2 to 3 minutes, stirring regularly, until the sauce is thickened. Remove from the heat.
Pull the meat from the shank bones and tear into bite sized pieces. If desired, clean the shank bones to use as decoration in the final pie. Return the lamb meat to the sauce along with the chopped parsley.
Preheat the oven to 415°F. Arrange four large ramekins on a baking sheet and spray with non-stick spray. Divide the lamb filling between the ramekins and set aside. On a lightly floured surface, roll each disc of dough out into a circle roughly 2 inches wider in diameter than the ramekins to allow for overhang. Use a small cutter or piping tip to cut a small circle from the middle of each circle of pastry.
Brush the rim of each ramekin with the beaten egg. If using the shank bone, arrange it in the middle of a ramekin. This will work best if the base of the shank bone is flat. If needed, press the larger pieces of lamb in the filling around the shank bones to help stabilize them. Lower the pastry over the top, threading the bone through the hole in the centre. Drape the pastry over the sides of the ramekins, pressing to seal the pies.
Brush the pastry with the remaining beaten egg. Bake the pot pies for 25 to 30 minutes until the pastry is golden brown and the filling is bubbling. Enjoy!