Preheat the oven to 375 degrees F. Unroll the piecrust and place in a 9-inch pie plate. Fold the overhang under and crimp the edge with a fork or your fingers. Bake the crust until light golden brown, about 10 minutes. Cool completely on a rack. (Leave the oven on.)
Whisk the corn syrup, brown sugar, salt, butter and vanilla in a medium bowl. Lightly beat the eggs in a small bowl, then whisk into the corn syrup mixture.
Finely chop 1/2 cup pecans and spread evenly over the piecrust. Roughly chop another
1/2 cup pecans and mix into the corn syrup mixture, then pour the filling into the crust. Arrange the remaining 1 cup pecans on top in a decorative pattern.
Bake the pie until a knife inserted into the center comes out clean, 40 to 50 minutes. Cool completely on a rack. Serve with whipped cream, if desired.