In a medium bowl, gently beat eggs. Don't over beat them. You don't want them to be frothy.
Stir in sugar and flour.
Melt the butter in a measuring cup (one that is also large enough for the syrup in the next step). Once melted, add the butter to the mixture.
Measure the light and dark corn syrups in the measuring cup, and add to the mixture. (The remaining butter in the measuring cup should allow the syrup to come out easily.)
Stir in the vanilla extract.
(Optional) Set aside about 1/2 cup whole pecans for the top. Using your method of choice, crush the remaining pecans into small pieces (but don't turn them to dust). One very easy way is to put them into a gallon-size zip-lock bag, squeeze out the air, and close it. Then beat them with a rubber mallet.
Put 1 cup of pecans (crushed, if you prefer) in the bottom of the pie crust and spread them around evenly.
Pour MOST of the mixture into the pie shell, then add the remaining 1/2 cup of whole pecans on top. Add the remaining mixture on top of the whole pecans. (This will make them look glazed.)
Tear some aluminum foil into strips and wrap the edges of the crust. This keeps it from burning.
Bake for 40 minutes, then remove the foil from around the crust. Continue baking for another 10-20 minutes. Check to see if its done by giving it a little shake; if there's no wiggle in the middle.. it's done.