Preheat the oven to 350°F (175°C).
In a mixing bowl, combine flour, butter, sugar, and salt. Mix until crumbly. Add egg yolk and cold water gradually until the dough holds together. Form into a disk, wrap in plastic, and refrigerate for 30 minutes.
Roll out the chilled dough on a floured surface and fit it into the pie pan. Trim the edges and prick the bottom with a fork. Bake in the preheated oven for 15-20 minutes or until lightly golden. Set aside to cool.
In a saucepan, whisk together sugar and cornstarch. Gradually stir in the water, then add the beaten egg yolks. Cook over medium heat, stirring constantly until thickened and bubbly.
Remove from heat and stir in butter, lemon juice, and lemon zest. Pour the mixture into the baked pie crust.
In a clean bowl, beat egg whites and cream of tartar until soft peaks form. Gradually add sugar, continuing to beat until stiff peaks form and glossy. Stir in vanilla extract.
Spread the meringue over the lemon filling, making sure it touches the crust to prevent shrinkage. Use a spatula to create peaks and swirls.
Bake the pie in the oven for 10-12 minutes or until the meringue is golden.
Allow the pie to cool at room temperature for at least 2 hours before serving.