Separate the egg yolks from the egg whites into 2 medium bowls.
Grate the rind of the lemons and set aside.
Squeeze the juice from the lemons.
Drain the pulp from the juice and set the juice aside.
Using a rotary beater or electric mixer, beat the egg whites with the cream of tartar and vanilla extract until soft peaks begin to form. Gradually beat in the sugar, beating until stiff and glossy peaks form and all the sugar is dissolved. Set the meringue aside.
Without washing the beater, beat the egg yolks until broken and combined.
Preheat the oven to 400 degrees.
In a saucepan, combine 1 - cup sugar, cornstarch and flour. Gradually add 1 ½ cups hot water, stirring constantly. Over medium heat, bring to boiling, stirring. Reduce heat, cook and stir until the mixture becomes shiny, about 2 minutes.
Quickly stir some of the hot mixture into the beaten egg yolks. Stir to blend well. Pour back into the saucepan, and stir well to blend.
Cook over low heat, stirring constantly, until mixture is cooked and thick, about 5 minutes.
Remove from heat. Stir in the lemon zest, lemon juice and butter.
Pour lemon filling into pie shell.
Spread meringue over lemon filling, carefully sealing to edge of the crust and swirling the top decoratively.
Bake until the meringue is golden brown, about 5 – 8 minutes.