Preheat the oven to 160°C/325°F/Gas Mark 3. Heat a heavy-based casserole dish with a lid over a medium heat. Add a couple of tablespoons of oil, then lightly dust the beef in the seasoned flour and add a batch to the heated oil. Quickly sear until golden brown on all sides, turning regularly with tongs. Transfer to a plate while you continue to cook the remainder. Add the tomato purée and garlic to the last batch of beef, stirring to coat, then transfer to a plate until needed.
Once you’ve cooked all of the beef, add a little more oil to the casserole dish and then sauté the onions and carrots for a couple of minutes. Pour in the wine, scraping the bottom of the dish with a wooden spoon to remove any sediment. Stir in the stout and add the thyme, bay leaves, brown sauce and canned tomatoes. Return the seared beef and any meat juices, then season to taste and place in the oven for 3 hours (or until meltingly tender but still holding its shape) stirring occasionally. Remove from the heat and leave to cool a little.
Drain the meat through a colander set over a large bowl to catch all the liquid. Remove the beef and vegetable mix, which should now be quite dense and discard the herbs. If necessary reduce the cooking juices in a clean pan to a gravy consistency and then set aside until needed.
Mix the beef and vegetable mixture with the sausagemeat until well combined. Roll out half of the rough puff pastry on a lightly floured board to a circle that is about 27 cm in diameter and place on a large non-stick baking sheet. Shape the beef and sausage mixture into a large dome shape about 23 cm in diameter and 6 cm in the middle at its highest.
Roll out the remaining pastry on a lightly floured board and use to cover the filling and base, brushing the edges with egg yolk to secure. Using a small sharp knife, make a small slit on top of the pie and then carefully make a pinwheel shape around the pie, gently twisting the knife as you draw it down the pastry rim to make an attractive pattern. Mark around the rim as well using the knife.
Brush the pithivier all over with the egg yolk, being careful not to let the egg yolk dribble down the edges of the pastry or it will prevent the pastry from puffing up and rising. Set aside to rest for 1 hour in the fridge (up to 4 hours is fine).
When ready to cook the pithiver, preheat the oven to 190°C/375°F/Gas Mark 5. Place the beef pie in the oven for 20 minutes, then reduce the oven temperature to 160°C/325°F/Gas Mark 3 and bake for another 40 minutes or until cooked through and golden brown.
Remove the beef pie from the oven and leave to rest for at least 10 minutes to allow the juices to settle. Reheat the gravy, stirring occasionally. Cut the rested beef pie into slices and arrange on warmed plates with a quenelle of mashed potatoes, honey-glazed carrots and a drizzle of the gravy.