Heat oil in a large casserole over medium heat. Add mince and cook, stirring with a wooden spoon to break up, until browned (6-8 minutes). Transfer mince to a bowl with a slotted spoon, leaving fat in pan.

Add beef cheek, in batches, to casserole in a single layer and brown over medium-high heat (4-5 minutes). Drain fat into a bowl and reserve. Deglaze pan with half the wine, scraping base, then transfer beef-cheek mixture to a bowl.

Wipe casserole clean, then return fat to casserole with onion, garlic, thyme and rosemary, stirring over low heat until onion is tender (10 minutes). Add celery and stir until tender (10 minutes). Stir in vinegar, half the stock and remaining wine, and simmer until flavours combine (5 minutes). Add tomato, remaining stock, beef-cheek mixture and mince, and season to taste with 1 tsp salt and ¾ tsp freshly ground white pepper. Simmer, covered, over low heat until beef cheeks are almost tender (about 1½ hours). Stir through mushrooms and simmer until softened (10 minutes).

Mix potato starch with 60ml (¼ cup) cold water in a bowl until smooth, then stir it through beef mixture to combine. Bring back to the boil, then remove from heat and transfer to a container to cool. Refrigerate overnight to chill and thicken. Meanwhile, prepare pastry.

Dice 135gm butter (refrigerate remainder). Combine flour, salt and diced butter on low speed in a food processor until it resembles sand (about 1 minute). Add vinegar and 305ml water, and mix on low speed until just combined and smooth (about 2 minutes). Shape dough into a 2cm-thick rectangle, wrap in plastic wrap and refrigerate overnight.

Roll out dough to a 20cm x 50cm rectangle. Cover and refrigerate. Place remaining chilled butter between two sheets of baking paper and beat with a rolling pin into a 20cm square. The butter should remain cold yet pliable. Place butter 10cm from one end of the pastry, fold bottom third of pastry over butter, then fold over remaining third of pastry to cover.

Turn dough 90 degrees clockwise and roll pastry away from you to a 20cm x 50cm rectangle. Fold top third of dough down, then bottom third over again. Turn 90 degrees and repeat, then wrap in plastic wrap and refrigerate overnight.

Repeat folding and rolling twice more (4 folds in total), then wrap in plastic wrap and refrigerate overnight.

Halve dough and roll one half to a 4mm-thick round, or cut individual 4mm-thick rounds (freeze remainder for another use for up to 2 months). Cover and refrigerate until required.

Combine flour, butter and salt in a food processor and pulse until it resembles fine crumbs with no lumps left. Combine vinegar with 60ml water and add to flour mixture. Pulse a couple of times until a dough forms.

Shape dough into a disc about 2cm thick, wrap in plastic wrap and refrigerate overnight.

Bring dough to room temperature (20 minutes), then roll out to a 4mm-thick round. If making individual pies, cut rounds about 1cm larger than pie tins.

Preheat oven to 200°C. Line a 25cm-28cm pie tin with pastry base dough, pressing well into the sides. Fill with chilled beef-cheek filling. Brush edge of pastry with eggwash and top with puff pastry lid. Pierce a hole in the centre to allow steam to escape. Trim edges, press all the way around to seal, and brush top with eggwash. Use trimmings to create decorations and brush with eggwash again. Bake until pie is deep golden, pastry is cooked through and filling is hot (40-45 minutes).