Place a rack in the center of the oven and preheat to 350°F (175°C). Line a baking sheet with parchment paper.
On a well-floured work surface, roll the puff pastry into a thin rectangle. The dough may seem pretty tough and difficult to roll out at first. Don’t be afraid to be firm with the dough: flip it upside down, turn it side to side, and pound it with the rolling pin to flatten it as you roll it into a long rectangle. Using a sharp knife, trim the edges of the rectangle to get rid of any rough edges.
Cut the dough into 8 equal squares. (It's easiest if you first halve the dough lengthwise into 2 strips and then cut each strip into 4 squares. If desired, use a ruler or a straight edge to measure the squares exactly so that the turnovers are easier to fill and the final pastry is uniform in size and appearance.)
Place about 1/3 cup (80 grams) pear compote off to the side in each square. (You'll probably have some extra pear compote. Enjoy it stirred into yogurt or dolloped on top of cheese.) Use the back of a spoon to spread the compote a little so it fills half the square diagonally and leave a little empty lip around the filling to allow for the sealing of the dough triangle. Using a pastry brush, lightly brush the empty pastry dough with the egg wash.
Carefully fold the egg-washed dough over the compote and use your fingers to pinch the turnover triangle together. Use the tines of the fork to firmly press the edges of the turnover together and make sure the turnover is well sealed. Repeat with the remaining dough and pear compote. Reserve any remaining egg wash.
Carefully move the turnovers to the prepared baking sheet. Add the cream to the remaining egg wash and whisk with a fork. Using a pastry brush, lightly brush the tops of the turnovers with the egg-cream mixture. Bake until the dough is entirely browned and baked through, 50 to 60 minutes. Look at the sides of the turnovers where the puff pastry has puffed up to make sure this part of the turnover is golden brown as well.
Remove from the oven and let the pear turnovers cool on the baking sheet on a wire rack for at least 1 hour before serving to allow the filling to cool. The turnovers are best enjoyed the same day you bake them, but they can be stored in an airtight container at room temperature for up to 2 days; refresh them in a 300°F (150°C) oven for 6 minutes.