Preheat oven to 375 degrees. with rack set in lowest position.
Using kitchen shears or a paring knife, trim dough to a 1-inch overhang. With floured fingers, fold overhang under itself to form a rim; pinch between thumb and forefinger to form a uniform edge around rim of pie plate. Crimp with fingertips. Transfer dough-lined pie plate to refrigerator.
Make filling: In a large bowl, whisk eggs, corn syrup, sugars, butter, vanilla, and salt until smooth; mix in pecans. Pour mixture into chilled pie crust; place pie plate on a rimmed baking sheet. Bake until filling jiggles slightly in the center when gently shaken, 50 to 60 minutes.
Cool pie completely in plate, 5 to 6 hours. Serve with whipped cream, if desired.