For the rough puff pastry, sift the flour into a bowl and make a well in the centre. Add the butter and salt and rub into the flour with your fingertips until the mixture resembles breadcrumbs.
Gradually add the ice-cold water, mixing until the dough comes together (be careful not to overwork the dough). Roll the dough into a ball, wrap in cling film and chill in the fridge for 20 minutes.
Remove the pastry from the fridge and unwrap it. Flour the work surface and roll out the pastry to a 40cm x 20cm/16in x 8in rectangle. Fold the pastry into thirds and give it a quarter turn. Roll the pastry out again into a 40cm x 20cm/16in x 8in rectangle as before and fold it into three again. Wrap the folded pastry in cling film and chill in the fridge for 30 minutes.
Remove the pastry from the fridge and unwrap it. Repeat the rolling out and folding process another two times, turning the pastry by a quarter each time. After folding it for the last time, wrap again in cling film and chill in the fridge until needed.
For the pie filling, place the beef, garlic, thyme, peppercorns and ale into a bowl. Cover with cling film and leave to marinate in the fridge for at least 2-3 hours, but preferably overnight.
Remove the beef from the marinade, pat dry with kitchen paper and dredge in the seasoned flour. Strain the marinade through a fine sieve into a clean bowl and set aside.
Heat the oil and one tablespoon of the butter in a flameproof casserole dish and fry the beef in small batches for 2-3 minutes each time, or until browned all over. Once the meat is browned, remove from the casserole dish and set aside.
Return the casserole dish to the heat and fry the mushrooms and shallots for 4-5 minutes, or until softened.
Return the beef and the reserved marinating liquid to the casserole and add the beef stock. Cover with a lid and gently simmer for 1½ hours, or until the beef is tender.
Strain off half of the cooking liquid from the casserole dish and set aside to make gravy for serving.
Crumble the Stilton into the casserole and stir until melted. Season, to taste, with salt and freshly ground black pepper and set aside to cool.
Preheat the oven to 180C/350F/Gas 4. Grease four 10cm/4in chefs' rings and dust each with flour.
Place the chefs' rings onto a baking tray and fill each with the beef and Stilton filling.
On a floured work surface, roll out the puff pastry to a thickness of about 2.5cm/1in. Cut out four circles of pastry large enough to cover the chefs' rings with a bit of overhang.
Brush the edges of the pastry with some of the beaten egg and place over the chefs' rings. Crimp the pastry to seal, then trim off any excess pastry, making sure there are no gaps between the chefs' rings and the pastry. Make a small hole in the middle of each pastry lid so allow steam to escape, then brush all over with the remaining beaten egg.
Bake the pies in the oven for 20-25 minutes, or until the pastry is crisp and golden-brown.
Meanwhile, place the reserved cooking liquid into a clean pan and simmer for 8-10 minutes, or until reduced to a gravy consistency. Stir in the remaining tablespoon of butter until melted, and the sauce is smooth and glossy. Keep warm.
For the celeriac and mustard mash, place the celeriac and potatoes into separate pans of cold water and bring to the boil. Reduce to a simmer and cook the celeriac for 15-20 minutes and the potatoes for 10-12 minutes, or until both are tender. Drain well, then place both the celeriac and potatoes to one pan and place back over the heat for a few minutes to drive off any excess moisture.
Mash the celeriac and potatoes together, then beat in the butter, the cream and the mustard until well combined. Season, to taste, with salt and white pepper.
For the honey-roasted beetroot, preheat the oven to 220C/425F/Gas 7.
Mix together the thyme, vinegar, olive oil and honey in a bowl until well combined.
Using a small melon baller or small spoon, scoop out balls of the beetroot and place into the bowl with the honey mixture and season, to taste, with salt and freshly ground black pepper.
Place the beetroot into a deep roasting tray and roast in the oven for 15 minutes, or until the beetroot is sticky and glazed.
To serve, transfer the pies onto a serving plate using a fish slice or spatula. Carefully remove the chefs' rings. Spoon the celeriac and potato mash on the side. Spoon the honey-roasted beetroot balls alongside and serve with a small jug of the gravy.