On a lightly floured surface, roll the dough disk into an 11-inch round that’s 1/8-inch thick (trim an edge to check thickness). Fold the dough in half and ease it into a 9-1/2-inch tart pan with a removable base, unfold it without stretching it, and press the dough firmly into the sides of the pan. Trim to the top of the pan by running the rolling pin over the top edge of the tart pan. (Save the scraps to make leaves for the pumpkin pie, if you like.) Chill the crust in the refrigerator or freezer for at least 30 minutes.
Position a rack in the middle of the oven and heat the oven to 350°F.
Cover the tart dough with foil, making sure to gently fold the foil completely over the top edge of the tart. Cover the bottom with a generous amount of pie weights (I use pennies, but raw rice or dried beans are fine). Bake until the crust no longer looks wet and is pale and golden in spots and on the edges, about 30 minutes. Remove the weights and foil, lightly prick the crust in several places with a fork (but don’t pierce through it), and bake uncovered until the crust is golden, about another 15 minutes.
In a medium bowl, mix the eggs and brown sugar. Add the corn syrup and beat well. Add the rum, melted butter, vanilla, and salt and beat well. Stir in the chopped pecans and scrape into the blind-baked tart shell. Arrange the pecans evenly. Bake until the filling begins to rise and is firm to the touch in the center, 23 to 27 minutes. Let cool before serving.