Begin by melting the butter-don’t burn it! While it is still hot, put it in a small mixing bowl and add the syrup and the sugar. Mix with a wire whip until smooth (until sugar has dissolved). Add the eggs and vanilla and whip for about 2 minutes. Pour this mixture into the pie shell and top with the pecan halves.
Bake at 325 degrees for 50 to 55 minutes or until a knife inserted in the center comes out clean. Cool in the refrigerator before serving.