On a lightly floured work surface, roll the pie crust into a 13-inch round, about 1/4-inch thick. Fit the crust into a 9-inch pie plate and trim the edges, leaving a 1-inch overhang. Fold the overhang underneath itself and crimp the edges. Refrigerate for at least 30 minutes before filling.
Roughly chop 2 cups of the pecans by hand or in a food processor; set aside. In a medium saucepan, melt the butter over medium heat. Whisk in the brown sugar until smooth. Remove from the heat and stir in the corn syrup, vanilla bean seeds and eggs. Fold in the chopped pecans and pour into the prepared pie shell. Arrange the remaining 1 cup pecan halves around the edge of the pie to make a decorative top.
Bake until the center is set, 60 to 70 minutes. Let cool completely.