In a large nonstick pan cook the apples, cranberries, sugar, cinnamon and nutmeg over medium heat stirring occasionally until the fruit is tender, about 10 minutes. Stir in the cornstarch mixture and cook for another 2 to 3 minutes, until the juices in the pan thicken. Set aside to cool.
Lay a sheet of phyllo onto a large cutting board and brush the dough with oil. Top with a second sheet and brush with oil. Sprinkle half the crushed cookies on top. Add another sheet of phyllo and brush with oil. Cut the phyllo into 4 long pieces. Put a small mound of the apple mixture about 1-inch from the bottom of 1 section and fold the phyllo over the mixture into a triangle-shaped pocket. Continue to fold to maintain the triangle shape so a turnover is formed. Repeat with the other 3 sections. Repeat the whole process again with 3 more sheets of phyllo so that you wind up with 8 turnovers. Be sure to reserve a little oil to brush the top of each turnover.
Spray a baking sheet with cooking spray, place the turnovers on the sheet, brush the tops with the remaining oil and bake for 20 to 25 minutes or until nicely browned. Serve warm.