Preheat oven to 400 degrees F. Line two baking sheets with parchment paper. For filling, in a large skillet cook ground lamb and onion over medium-high heat until meat is browned. Stir in next five ingredients (through pepper). Cook 5 to 8 minutes or until mushrooms are tender, stirring occasionally. Stir in hard-cooked egg and saffron. Remove from heat; cool 10 minutes.
Meanwhile, on a lightly floured surface, unfold 1 puff pastry sheet at a time; roll into a 14x10 1/2-inch rectangles. Cut each rectangle into twelve 3 1/2-inch squares (24 total).
Spoon a scant 2 tablespoons of the filling onto each pastry square. Combine egg and water. Lightly brush edges of pastry squares with egg mixture. Fold one corner of each square diagonally over filling to make a triangle. Press edges together with a fork to seal. Place on the prepared baking sheets. Lightly brush tops and sides with egg mixture.
Bake 18 to 20 minutes or until pastries are puffed and golden brown. Let stand 5 minutes before serving.