Heat oven to 400°F. Melt butter in a large nonstick skillet over medium heat. Add apples, currants, sugar and nutmeg. Cook, stirring, 4 to 5 minutes or until apples are tender. Remove from heat and let cool slightly. Stir in cream cheese, egg yolk, flour and lemon zest.
Unfold one of the pastry sheets on a lightly floured surface. Roll out slightly to measure 12 inches square. With pizza cutter or sharp knife, cut pastry into 9 equal squares (each 4 inches per side).
Spoon 1 tablespoon apple mixture into the center of one square. Fold in half diagonally to form a triangle. Seal open edges with a fork and transfer to an ungreased baking sheet. Brush with a little egg white. Repeat with remaining squares.
Bake at 400°F for 14 to 15 minutes, until puffed and nicely browned on top. While turnovers bake, repeat rolling, filling and folding with remaining pastry sheet, filling and brushing with egg white.
Remove turnovers from baking pans to wire rack to cool, at least 10 minutes. Best if served same day as baking; reheat in 350°F oven for 5 minutes.