Remove puff pastry from the freezer and thaw according to instructions while making and cooling the pear filling.
In a medium pot, melt 1 Tbsp butter over medium heat. Add diced pears and cook, stirring occasionally until softened (5 min).
Reduce heat to low and stir in 1/4 cup brown sugar, cinnamon, ginger and salt. Continue to simmer 3 minutes until pears are soft and caramelized. Remove from heat and set aside to cool.
Use a rolling pin to roll the first sheet of thawed pastry to an 11" square. With a pizza cutter, cut into 4 equal-sized squares. Place a ¼ cup cooled pear mixture in center of each square, leaving at least a 1/2" border. Filling is juicy so make sure to not get too much liquid when scooping mixture.
Thoroughly Beat together 1 egg and 1 Tbsp water. Brush eggwash lightly on edges of the pastry (just enough to seal), bring the edges together and crimp tightly along the edges with a fork to seal.
Transfer to a parchment-lined baking sheet, keeping them at least 1" apart. With a paring knife, cut 2-3 small slits in the top of each turnover. Refrigerate for 20 minutes (this helps the filling from leaking out.)
Preheat oven to 400F. Brush the tops with egg wash and bake 20-23 minutes or until golden and puffed.
While turnovers are still warm, stir together powdered sugar, vanilla, and heavy whipping cream (adding to your desired consistency) and drizzle glaze over turnovers.