Mix sugar, brown sugar, salt, corn syrup, butter, eggs, and vanilla together in a bowl.
Pour chopped pecans in the bottom of the unbaked pie shell.
Pour syrup mixture over the top. Cover top and crust lightly/gently with foil. Bake pie at 350º for 30 minutes. Remove foil, then continue baking for 20 minutes, being careful not to burn the crust or pecans.
NOTE: PIE SHOULD NOT BE OVERLY JIGGLY WHEN YOU REMOVE IT FROM THE OVEN. If it shakes a lot, cover with foil and bake for an additional 20 minute or until set. Required baking time seems to vary widely with this recipe. Sometimes it takes 50 minutes; sometimes it takes 75!
Allow to cool for several hours or overnight. Serve in thin slivers.