Rub the venison with oil and seasoning, then sear on all sides in a hot pan.
Sauté shallots in butter until soft, then add mushrooms and thyme and cook for 8 minutes.
Add port to the mushrooms and cook until almost dry before cooling the mixture.
Overlap prosciutto slices on clingfilm and spread with the mushroom mixture.
Spread pâté over the venison, place on the mushrooms, wrap tightly with clingfilm, and chill for 30 minutes.
Preheat the oven to 200°C.
Cut two pieces of puff pastry slightly larger than the wrapped meat.
Place the meat onto one pastry sheet and brush with beaten egg.
Cover with the second pastry sheet, seal the edges, trim excess, and bake for 15 minutes.
Lower the oven to 150°C and cook for 10 more minutes.
Remove from the oven and rest before slicing.