Place the unbaked pie crust in a 9-inch pie dish. Chill in the refrigerator while you prepare the filling.
In a large bowl, mix together granulated sugar, brown sugar, salt, and cinnamon if using. Stir in the corn syrup, melted butter, eggs, and vanilla extract until smooth. Gently fold in the pecans. Pour the filling into the chilled crust.
Bake at 425°F for 10 minutes, then lower the oven temperature to 350°F and bake for 40-50 more minutes, or until set. It should not be super jiggly. If the pie top browns too quickly, cover it loosely with aluminum foil during baking.
Allow the pie to cool completely before serving. If desired, serve with whipped cream.