Make sure all the filling ingredients are completely cold before assembling.
Roll out the puff pastry to about 5 mm (¼ inch) thick.
Cut out four 15 cm (6 inch) discs and four 10 cm (4 inch) discs.
Line a ladle or small bowl with cling film. This will help form the filling into a neat dome.
Lay 2 cabbage leaves inside, allowing enough overhang to fold over the filling.
Add a layer of the mushroom mixture, followed by spinach and a slice of chicken liver pâté. Top with 3 pigeon breasts.
Fold the cabbage leaves over the filling to enclose it completely and press gently to form a compact dome.
Turn the dome out onto a tray and repeat to make 4 in total.
Lay the four smaller pastry discs on a lined baking sheet.
Place one filling dome in the center of each disc, leaving about a 2 cm (¾ inch) border around the edge. Brush the exposed pastry border with beaten egg.
Place the larger pastry discs over the filling and press the edges down firmly to seal. Crimp the edges with a fork.
Decorate the tops by lightly scoring the pastry with a knife, or add a pastry lattice if desired.
Cut a small hole in the top of each pithivier to allow steam to escape. Brush all over with beaten egg.
If using a lattice, tuck a few reserved thyme leaves between the pastry strips.