Lightly flour the countertop. Roll puff pastry so there are no seams. Cut into 4 squares.
In a bowl, combine salmon, mushrooms, pickle relish, rice, scallions, parsley, salt, and pepper. Place 1 tablespoon of filling in the center of each square. Brush inside edges of puff pastry with egg wash and fold over to make a triangle. Using a fork, seal the edges. Poke a slit or two in the top of each turnover. Brush tops with egg wash. Bake in oven for 30 minutes or until golden brown.