Roll out 1 disk of dough into a 12-inch round on a lightly floured surface. Fit into a 9-inch pie plate, and trim edge of dough to rim. Roll out remaining disk of dough to a 12-inch round. Transfer to a parchment-lined baking sheet, and refrigerate, along with dough in pie plate, until firm, about 1 hour.

Preheat oven to 350 degrees. Melt butter in a bowl set over a saucepan of simmering water; remove from heat. Whisk in brown sugar, flour, spices, salt, vinegar, and 1 cup water. Lightly beat 2 eggs, and whisk into mixture. Return bowl to pan of simmering water, and cook, stirring often, until mixture is thick enough to coat the back of a spoon, 10 to 12 minutes. Remove from heat, and let cool to room temperature, about 20 minutes, stirring occasionally.

Pour filling into crust, and place top crust over filling. Trim excess, leaving a 1/2-inch overhang. Fold under bottom crust. Press to seal, and crimp as desired. Beat remaining egg with remaining teaspoon water; brush top of pie with egg wash, and sprinkle with turbinado sugar. Use a sharp knife to slash 6 vents radiating out from center of pie. Bake pie until golden and surface has puffed, about 45 minutes. Let cool on a wire rack 45 minutes. Serve slightly warm with ice cream.