With a pastry cutter or using two knives mix the flour with butter. Add egg yolks and a pinch of salt and sugar. Knead dough until smooth, wrap in cling film and refrigerate for 30 minutes.
Preheat the oven to 200 C / Gas 6. Grease 2 loaf tins.
Heat the oil in a large pan and saute the fish, onion and mushrooms until fish flakes and onion is tender. Stir in eggs, rice and chopped parsley, and season to taste.
Roll out the chilled dough into 4 rectangles, two larger to fit the bottom and sides of the loaf tins, and two smaller for the covers. Line the bottom and sides of the loaf tins with the larger rectangles. Spoon the stuffing into the prepared loaf tins, cover with smaller rectangles and pinch the edges to seal. If there's any dough left, you can arrange cut out pieces in a decorative pattern on top. Brush with a beaten egg.