Preheat the oven to 350°. Spread the pecans in a pie plate and toast for about 8 minutes, until fragrant. Let cool.
Increase the oven temperature to 400°. On a floured work surface, roll out the dough to a 13-inch round; patch any cracks. Fold the round in quarters and transfer to a 9-inch glass pie dish; unfold the pastry and gently press it into the pie plate. Using scissors, trim the overhanging dough to 1/2 inch. Tuck the edge of the dough under itself and crimp decoratively. Line the dough with foil, shiny side down, and prick all over with a fork, piercing the foil and pie dough. Freeze for 15 minutes.
Fill the pie with pie weights or dried beans and bake in the lower third of the oven for 30 minutes. Remove the foil and weights. Return the crust to the oven and bake until lightly browned, about 12 minutes.
Meanwhile, in a heatproof bowl, combine the brown sugar, corn syrup, butter and salt. Set the bowl over a saucepan filled with 1 inch of simmering water and whisk in the eggs 1 at a time. Cook, whisking gently, until the filling is warm to the touch. Remove from the heat and whisk in the rum.
Arrange the pecans in the pie shell and scatter the crystallized ginger on top. Pour the filling over the pecans. Bake for about 25 minutes, until the filling is jiggly but not cracked; cover the edge of the crust with strips of foil halfway through baking to prevent over-browning. Let the pie cool on a wire rack. Cut into wedges and serve.