Once the coals are ready, arrange the sausages in the grill basket and cook them on the Compact Braai, turning regularly. Check the centre of the thickest sausage with a clean food thermometer: it should reach 75°C before you use it in the pie. Browning alone does not confirm it is cooked through.
Transfer the cooked sausages to a clean board and split each one lengthways.
Let the empty basket cool before applying cooking oil spray, away from the heat or flames. Lay two puff pastry sheets side by side in the basket to form two bases, leaving enough pastry around the filling to seal the edges. Keep pastry chilled until assembly.
Spread barbecue sauce over the bases. Arrange the cooked sausage halves in an even layer. Cover each base with six cheese slices, then add more barbecue sauce.
Cover each filled base with a sheet of puff pastry. Fold the edges underneath and crimp all the way around each parcel with a fork to seal.
Beat the two eggs and brush the exposed pastry with egg wash. Secure the parcels in the basket, turn it over, carefully open the other side and brush that pastry too. Close and secure the basket again.
Put the basket on the Compact Braai over steady coals and turn regularly. Adjust the heat if the surface darkens before the pastry is cooked. Continue until the pastry is cooked through on both sides and at the sealed edges, with the cheese melted and the filling piping hot.
Transfer the pie to a clean board. Let the filling cool enough to eat, then cut into portions. Serve with extra barbecue sauce if you like.