Preheat the oven to 425 degrees. Place rack in lowest position possible in oven.
Combine the pecans, brown sugar, corn syrup, butter, flour and salt in a heavy saucepan over medium heat. Bring to a boil, stirring constantly. Remove from heat. Cool 15 minutes.
Whisk together the eggs and vanilla. Stir about 1/2 cup of the hot sugar mixture into the eggs to temper them, then stir this mixture into the hot sugar mixture.
Pour the filling into the pie shell. Bake 10 minutes. Reduce the oven temperature to 325 degrees. Bake until the custard has set and the nuts rise to the top, about 30 to 40 minutes. If the crust browns too quickly, cover with foil. Transfer to a rack and let cool.
Serve with ice cream or whipped cream. Serves 8.