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Step 1
For the filling: Preheat your oven to 325 degrees F (160 degrees C) and heat a large heavy-bottomed pot over medium high.
Step 2
Add the oil to the pan, season the beef well with salt and pepper and dust with 2 tablespoons of the flour. Sear the beef in two or three batches until browned on each side, about 8 minutes total, removing the meat to a dish once seared.
Step 3
Add the butter to the pan and turn the heat down to medium. Add the carrots, celery and onions, season with salt and pepper and cook for 5 minutes or until softened and lightly brown. Add the garlic and cook for an additional minute or two. Add the tomato paste, brown sugar, Worcestershire sauce, thyme, bay leaves and beef. Scatter with remaining 2 tablespoons flour and stir well to combine. Add the stout, scraping the bottom of the pan to release any brown bits. Add the beef stock and potatoes and bring the mixture to a boil. Cover with a tight-fitting lid, transfer to the oven and cook for 1 1/2 to 2 hours or until the beef is tender.
Step 4
Transfer the beef and vegetables to a bowl, leaving the braising liquid in the pan. Place the braising liquid over high heat. Bring to a boil to reduce by about half. Keep warm over low heat or if prepping in advance, transfer to a container and place in the fridge for up to 2 days or freezer for 3 months.
Step 5
Season the beef and veg with more salt and pepper, if needed, and set aside to cool completely.
Step 6
Meanwhile, make the pastry by combining the butter and water in a large saucepan. Bring to a boil and melt the butter. Remove from the heat and add the flour and salt. Stir to bring together and turn out onto a lightly floured surface. When cool enough to handle, knead the dough until very smooth and a little elastic. Wrap in plastic and set aside to rest for 30 minutes.
Step 7
When ready to bake, set a rack to the bottom position and preheat your oven to 400 degrees F (200 degrees C). Wrap the outside of a 9-inch springform pan with aluminum foil.
Step 8
On a lightly floured surface, divide the pastry in two, one slightly smaller than the other. Roll the larger piece of pastry out to 1/2-centimeter (1/4-inch) thick and transfer to the springform pan, lining the bottom and up the sides. Fill with the cooled beef and veg. Roll out the remaining pastry and drape over the filling, crimping and sealing the edges with a fork or by pinching with your fingers. Beat together the egg and milk and brush over the top of the pie. Cut a vent into the center of the pastry and place on a large baking sheet.
Step 9
Bake for 20 minutes then reduce the heat to 350 degrees F (175 degrees C) and continue to bake for 30 to 35 minutes or until the pastry is golden.
Step 10
Allow the pie to cool for 10 minutes before unmolding, slicing, and serving with the reduced braising liquid as a gravy.