Make the crust: Pulse the flour, granulated sugar and salt in a food processor until combined. Add the butter and pulse about 10 times until it looks like cornmeal with pea-size bits of butter. Add the egg and pulse 1 or 2 more times. If the dough is very dry, add the water. Pulse 8 to 10 times until the dough starts to clump together and there is no visible flour. Turn out the dough onto a piece of plastic wrap and form into a disk; wrap tightly. Refrigerate until firm, at least 1 hour or overnight.
Roll out the dough on a lightly floured surface into a 12-inch round. Ease into a 9-inch pie plate. Trim the edges, leaving a 1-inch overhang, then tuck the overhanging dough under itself; crimp the edges with a fork. Freeze until firm, about 30 minutes.
Meanwhile, position racks in the middle and lower thirds of the oven; preheat to 375˚. Spread the pecans on a baking sheet and bake on the middle rack until toasted, 10 to 12 minutes. Let the nuts cool slightly, then roughly chop.
Line the chilled pie crust with parchment paper or foil and fill with dried beans or pie weights. Place the pie crust on a baking sheet and bake on the middle rack until the dough is dry and set around the edges, 20 to 25 minutes. Remove the parchment and beans and continue baking until the crust is light golden brown all over, 10 to 15 more minutes.
Meanwhile, make the filling: Combine the butter, brown sugar, corn syrup, bourbon and salt in a medium saucepan. Bring to a boil over medium heat, stirring; boil 1 minute. Remove from the heat and stir in the chopped pecans and vanilla bean paste. Let cool slightly, about 5 minutes. Whisk the eggs into the filling until smooth, then pour the filling into the hot crust. (If the crust has cooled, return it to the oven for 5 minutes to warm through before filling.)
Reduce the oven temperature to 350˚. Bake the pie (on the baking sheet) on the lower oven rack until the edges are set but the center is still slightly loose, 40 to 45 minutes. (If the crust is getting too dark, cover loosely with foil.) Transfer the pie to a rack to cool completely.