- Heat the oven to 350°F and arrange a rack in the lower third. Coat a 9-inch pie plate with butter; set aside.
- On a lightly floured surface, roll out the dough to about 12 inches in diameter and between 1/4 and 1/8 inch thick. Without stretching the dough, line the prepared pie plate and trim to leave a 3/4-inch overhang. Fold the overhanging dough underneath itself, crimping the edges with two fingers along the rim of the pie plate to form a high, fluted border. Cover the pie shell in plastic and chill until needed.
- Place the sugar, syrup, butter, and rum in a large saucepan over medium heat and bring to a boil. Boil for 1 minute, stirring constantly and scraping back in any foam that clings to the sides of the pan. Remove the pan from the heat and set aside to cool to lukewarm, at least 15 minutes.
- Beat the eggs in a small bowl until the yolks and whites are broken up and incorporated, then beat into the cooled syrup. Add the pecans, vanilla, and salt and stir to combine. Pour into the chilled pie shell.
- Bake until the filling is set but still slightly wobbly in the center, about 50 minutes. Cool the pie completely on a wire rack. Serve at room temperature with whipped cream or vanilla ice cream, if so desired.