Preheat oven to 350°F. Line 9-inch pie pan with pastry; trim and flute edges.
Beat eggs in a small bowl until frothy; set aside. Combine sugar and water in 2-quart heavy saucepan. Place over medium heat, stirring until sugar dissolves. Bring to a full rolling boil and cook for 3 minutes. Gradually stir hot syrup into eggs. Add pecans, butter and vanilla to mixture. Pour filling into pastry-lined pie pan.
Bake at 350°F for 45 to 50 minutes or until set. Cool.
Makes 8 to 10 servings.
To make a Walnut Pie, substitute walnut halves for pecans. To make a Toasted Almond Pie, substitute whole toasted almonds for pecans.