Preheat the oven to 400° and place the oven rack in the lower third of the oven.
Place the rolled pie crust into a 9-inch pie pan and either flute the edges or make a decorative edge. Place in the fridge until you are ready to bake the pie.
In a large bowl beat together the eggs, brown sugar, salt, vanilla, and corn syrup. Stir in the walnuts and add the filling to the chilled pie crust.
Bake for 15 minutes at 400° and then lower the heat to 350° and bake for another 35-40 minutes, until the center of the pie is slightly jiggly but set. If the top of the pie or the crust seems to be getting too dark too fast, place a sheet of foil gently over the whole pie to keep it from burning while the pie finishes baking.