Thaw phyllo pastry according to package directions.
Beat cream cheese at medium speed with an electric mixer until creamy; add 1/2 cup sugar, cinnamon, and nutmeg, and beat until smooth.
Toss apple with lemon juice. Stir in dates and pecans. Fold cream cheese mixture into apple mixture until combined.
Unfold phyllo pastry on a lightly floured surface. (Keep remaining sheets covered.) Stack 4 phyllo sheets on a baking sheet, brushing between each sheet with melted butter and sprinkling evenly with additional sugar. Carefully spread about one-third of apple mixture over phyllo, leaving a 1 1/2-inch border around edges; repeat procedure twice, ending with apple mixture.
Layer remaining 2 phyllo sheets, brushing with butter and sprinkling with sugar. Cut in half crosswise. Place 1 half on top of each other. Using a sharp knife, cut into 1-inch-wide strips. Place strips diagonally on top of apple mixture. (You may not need all the strips.) Fold over 1 1/2-inch borders of pastry, pressing gently to seal.
Bake at 350° for 40 minutes or until golden. Serve warm.