Cut pastry into 8 wedges. On floured surface, roll in 6-inch circles. Place on baking sheet; cover; chill.
Combine cheeses, sugar, cinnamon and vanilla in food processor or mixer bowl. Whirl or beat until smooth. Beat in egg white until blended. Stir in by hand apricot and pecans if using.
Heat oven to 350°F. Coat 2 baking sheets with cooking spray.
Brush beaten egg in 1-inch border around edge of pastry circle. Spoon scant 1/3 cup filling in center. Fold over, forming half-moon; crimp edges. Place on baking sheet. Repeat with remaining circles and the filling. Brush with egg; top with sugar.
Bake in 350°F oven 25 minutes, until golden. Cool on racks 15 minutes. Serve with puree.
Place flour and salt in food processor. Pulse to combine. Add butter and shortening. Pulse until texture of coarse meal.
With on-and-off pulses, add water just until mixture comes together. Pinch small handful of dough together; if it doesn't stick together, add another tablespoon water and process until combined.
Puree raspberries in blender. Strain to remove seeds. Refrigerate until serving time.