Place the folded sheet of frozen puff pastry on a clean towel and cover. Thaw at room temperature for 30 to 40 minutes.
Heat oven to 400ºF.
Gently unfold the thawed puff pastry sheet and crimp the seams together with your fingertips. Lightly dust the counter with flour. Using a rolling pin, roll the pastry in each direction to smooth out the seams. Cut into 4 equal squares.
In a bowl, combine the salmon, rice, mushrooms, pickle relish, scallion, and parsley. Taste and season with salt and pepper, as desired.
Place 2 tablespoons of filling in the center of each square. Brush the inside edges of the 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 and brush with egg wash. Bake until golden brown, about 30 minutes. Let cool for 10 minutes before serving.