To make pie filling, coo9k rice in boiling salted water for 8 minutes or until just cooked. Rinse under cold running water, then drain well. Transfer to a bowl with the cream, butter, dill, parsley and lemon zest, Then season with sea salt and freshly ground black pepper and stir to combine.
Divide pastry in half and roll out 1 portion to a 25cm x 30cm rectangle. Place on a baking tray lined with baking paper and spread over half the rice mixture. Top with salmon, then soft-boiled egg. Brush pastry edges with water, then spread remaining rice over filling. Roll out remaining pastry to a 25cm x 30 cm rectangle, then cut with a lattice cutter (available at kitchenware shops). Place on top of rice mixture, pressing edges to seal. Alternatively roll out remaining portion of pastry and place over filling, pressing edges to sea. Refrigerate pie for 30 mins.
Preheat oven to 180°c. Brush top of pastry with beaten egg, then bake pie for 25-30 minutes until puffed and golden.
To make caper butter sauce, melt butter, without stirring, in a frypan over low heat, skimming any foam from surface. Remove from heat and stand for 1 minute or until milk solids sink to bottom. Carefully pour liquid clarified butter into a jug, discarding solids. Stir in capers and dill.
Slice pie and serve with the warm caper butter sauce.