1To make the crust, in a food processor, briefly pulse together the flour and salt. Add the butter and pulse until the mixture forms lima bean–size pieces (three to five 1-second pulses). Add ice water 1 tablespoon at a time, and pulse until the mixture is just moist enough to hold together. Form the dough into a ball, wrap with plastic, and flatten into a disc. Refrigerate at least 1 hour before rolling out and baking (or up to a week, or freeze for up to 4 months).
2On a lightly floured surface, roll out the piecrust to a 12-inch circle. Transfer the crust to a 9-inch pie plate. Fold over any excess dough, then crimp as decoratively as you can manage.
3Prick the crust all over with a fork. Freeze the crust for 15 minutes or refrigerate for 30 minutes. Preheat the oven to 400°F. Cover the pie with aluminum foil and fill with pie weights (you can use pennies, rice, or dried beans for this; I use pennies). Bake for 20 minutes; remove the foil and weights and bake until pale golden, about 5 minutes more. Cool on a rack until needed.
4To make the filling, in a medium saucepan over medium-high heat, bring the maple syrup, Demerara sugar, and star anise to a boil. Reduce to a simmer and cook until the mixture is very thick, all the sugar has dissolved, and the syrup measures 1 cup, 15 to 20 minutes. Remove from the heat and let sit for 1 hour for the anise to infuse.
5While the syrup is infusing, toast the nuts. Preheat the oven to 325°F. Spread the pecans out on a baking sheet and toast them in the oven until they start to smell nutty, about 12 minutes. Transfer to a wire rack to cool.
6Remove the star anise from the syrup. Warm the syrup if necessary to make it pourable but not hot (you can pop it in the microwave for a few seconds if you’ve moved it to a measuring cup). In a medium bowl, whisk together the syrup, eggs, melted butter, rum, and salt. Fold in the pecan halves. Pour the filling into the crust and transfer to a rimmed baking sheet. Bake until the pie is firm to the touch but jiggles slightly when moved, 35 to 40 minutes. Let cool to room temperature before serving with whipped crème fraîche.