Most any pie pastry will do. Roll the dough into a 13-inch circle and line a 9-½-inch deep-dish pie plate with it, forming the overhanging dough into an upstanding rim. Chill and partially prebake the shell. Then cool the shell. For more about creating a rim and prebaking, see Everyday Baking.
Preheat the oven to 350°F. Using an electric mixture, beat the eggs and brown sugar in a large bowl until evenly blended. Add the corn syrup, melted butter, vanilla, and salt and beat again, briefly, until evenly blended. Stir in the peanuts. Carefully pour the filling into the cooled pie shell. Bake the pie on the center oven rack for 30 minutes. Rotate the pie 180 degrees and bake for 20 to 25 minutes more. When done, the pie will be “set,” meaning that it will not move in waves when the pie plate is nudged. Thoroughly cool the pie on a rack. Serve at room temperature or cover with loosely tented foil and refrigerate for 1 or 2 hours before serving.
I often recommend rotating pies 180 degrees midway through the baking. The back of most ovens is typically hotter than the front. Rotating helps baked goods to cook evenly and balances the surface browning.