In a medium bowl, whisk together the egg yolks and sweetened condensed milk until well blended. Gradually whisk in the key lime juice. Pour into the graham cracker crust.
Bake for 25 minutes in the preheated oven, or until the center is set when the pie is gently shaken. Set aside. Reduce the oven temperature to 325 degrees F (165 degrees C).
In a large clean bowl, whip egg whites, key lime juice, with the cream of tartar until soft peaks form. Gradually sift in the confectioners' sugar, while continuing to whip to stiff peaks. Spoon on top of the slightly cooled pie, sealing the meringue to the edges of the crust.
Bake for about 10 minutes in the preheated oven, until the meringue is lightly toasted. Cool to room temperature before refrigerating. Chill for at least 2 hours before serving.