Heat oven to 375°F. Lightly grease large baking sheet; set aside.
Combine all pastry ingredients in large bowl; beat at low speed, scraping bowl often, until well mixed.
Divide dough in half; shape each half into a ball. Flatten each into 1/2-inch thick rectangle. Wrap each in plastic food wrap; refrigerate 15 minutes.
Meanwhile, combine all filling ingredients in small bowl; set aside.
Roll out half of dough on lightly floured surface into 12x8-inch rectangle. (Use a ruler or straight edge to gently push in sides to keep straight.) Cut into 6 (4-inch) squares. Repeat with remaining dough. Press or roll out each to 5-inch square. Spoon filling evenly over center or each square.
Beat egg white in small bowl with wire whisk until foamy. Lightly brush inside edges of pastry square with beaten egg white. Bring two opposite points together to form triangle; pinch edges to seal. Crimp edges with fork. Place onto prepared baking sheets.
Brush top of turnovers with remaining egg white; sprinkle with sugar, if desired. Carefully prick in 3 places with fork. Bake for 20 to 23 minutes or until light golden brown. Remove to wire cooling racks. Cool 10 minutes.
Meanwhile, combine powdered sugar; lemon juice, ginger and enough water for desired glazing consistency in small bowl; drizzle over warm turnovers.
Serve warm or cooled. Store cooled turnovers in container with tight-fitting lid.
*Substitute apple pie filling.