Heat oven to 400° F.
On a lightly floured surface, roll the pastry dough into a round about 13-inches in diameter. Lower dough carefully into a deep 9-inch pie dish, pressing it into place gently with your fingers. Let excess dough rest lightly over the edge of the plate, untrimmed. Place dish into the refrigerator to chill as you prepare the filling.
In a large bowl, gently toss the pears, figs, lemon juice, lemon zest, brown sugar, cinnamon, cardamom, salt, and cornstarch. Spoon the fruit mixture into the chilled pie plate. Fold the edges of the pie dough over the filling in rustic pleats, leaving the center bare. Brush dough with egg and sprinkle generously with turbinado sugar.
Bake until golden, about 20 minutes, then lower heat to 375° F and continue to bake until juices are bubbling, about 40 minutes more. If crust darkens too deeply, tent with tin foil. Remove from oven and let cool at least 2 hours before serving.