Preheat oven to 350°F with a baking sheet on middle rack.

Roll out dough on a lightly floured surface with a lightly floured rolling pin into a 12-inch round and fit into a 9-inch pie plate. Trim edge, leaving a 1/2-inch overhang.

Fold overhang under and lightly press against rim of pie plate, then crimp decoratively. Lightly prick bottom all over with a fork. Chill until firm, at least 30 minutes (or freeze 10 minutes).

Meanwhile, melt butter in a small heavy saucepan over medium heat. Add brown sugar, whisking until smooth. Remove from heat and whisk in corn syrup, vanilla, zest, and salt. Lightly beat eggs in a medium bowl, then whisk in corn syrup mixture.

Put pecans in pie shell and pour corn syrup mixture evenly over them. Bake on hot baking sheet until filling is set, 50 minutes to 1 hour. Cool completely.