In a food processor, combine the flour, sugar, and salt and pulse while adding the butter, a few pieces at a time. Add the ice water, 1 tablespoon at a time, until a dough starts to form.
Shape the dough into a ball. Do not handle more than necessary. Wrap with plastic and refrigerate for at least 4 hours, but best if overnight.
Preheat the oven to 350°F.
In a medium bowl, combine the brown rice syrup, soy milk, paht, brown sugar, melted butter, salt, vanilla, chopped pecans, and potato starch.
Place the pie dough between two sheets of parchment paper. Using a rolling pin, roll out the pie dough gently until it is large enough to line a 9-inch pie pan. Ease the crust into the pan and trim any excess dough at the edges with kitchen shears or a sharp paring knife. Pour in the filling. Top the filling with pecan halves.
Transfer the pie to the oven and bake until the pie filling sets (i.e., doesn’t jiggle too much), 1 hour to 1 hour 15 minutes. Cool the pie on a wire rack for 2 hours before serving.
