For the crust: Preheat the oven to 350 degrees F. Lightly spray a 9-inch-diameter glass or ceramic pie dish with vegetable oil cooking spray.
In a food processor, blend the flour, sugar and salt until combined. Add the butter and mascarpone cheese and blend until moist clumps form. Gather the dough into a ball. Drop 2-inch pieces of dough over the bottom and sides of the pie dish. Using moist fingertips press the dough together to form a smooth crust. Using the tines of a fork, prick the dough all over.
Bake the crust until the edge is browned and the center of the crust is pale golden, about 25 minutes. Transfer the crust to a work surface. Brush the bottom and sides of the crust with apricot preserves.
For the filling: In a food processor, combine the pumpkin and persimmon. Blend until smooth. Add the sugar, mascarpone, cream, cornstarch, cinnamon, salt and eggs. Blend until smooth. Pour the filling into the cooked crust.
Bake the pie until slits or cracks appear around the edge and the center is set, about 35 minutes. Cool the pie on a rack. (Can be made 1 day ahead. Bake and cool to room temperature. Cover loosely with plastic wrap and refrigerate.)
Just before serving, dust the top of the pie with powdered sugar. Cut into wedges and serve.
To remove the pulp from Hachiya persimmons, remove the top with a knife and scoop out the pulp with a spoon.