Make the crust: Pulse the flour, sugar and salt in a food processor. Add about one-third of the butter and pulse until the mixture looks like cornmeal. Add the remaining butter and pulse 3 times, or until the mixture looks like coarse meal with pea-size bits of butter. Drizzle in 3 tablespoons ice water and the vinegar and pulse 3 or 4 times, just until combined (do not let the dough come together into a ball). Pinch the dough between your fingers; if it doesn't hold together, add up to 2 more tablespoons ice water, 1/2 tablespoon at a time, pulsing. Turn out onto a sheet of plastic wrap and pat the dough into a disk; wrap tightly and refrigerate until firm, at least 1 hour and up to 1 day.
Roll out the dough into an 11-inch round on a lightly floured surface. Ease into a 9-inch pie plate. Fold the overhanging dough under itself and crimp the edges with your fingers. Refrigerate the crust 1 hour.
Place a baking sheet on the middle oven rack and preheat the oven to 375 degrees F. Make the filling: Whisk the flour, brown sugar and butter in a large heatproof bowl; set aside 2/3 cup of the mixture for topping. Whisk the egg, molasses and baking soda into the remaining brown sugar mixture, then whisk in 3/4 cup boiling water until smooth.
Pour the filling into the chilled crust. Sprinkle the reserved brown sugar mixture on top. Carefully transfer the pie plate to the hot baking sheet and bake 10 minutes. Reduce the oven temperature to 350 degrees F and continue baking until the crust is golden and the filling is firm, 40 to 45 more minutes. Transfer to a rack to cool; serve warm or at room temperature.