Preheat the oven to 375°F.
Make the crust dough: In a bowl, stir together flour, sugar, and salt. Cut in the cold butter until pea-sized. Add 4 tablespoons ice water and mix. Add more water 1 tablespoon at a time only if needed.
Chill the dough for 30 minutes, wrapped.
Roll and shape: Roll into a 12-inch circle and fit into a 9-inch pie dish. Trim and crimp edges.
Blind bake: Line with parchment and fill with pie weights. Bake 15 minutes. Remove weights and parchment, prick bottom lightly, and bake 10 to 12 minutes more until lightly golden.
Start the lemon filling: In a saucepan, whisk sugar, cornstarch, and salt. Slowly whisk in water until smooth.
Cook until thick: Place over medium heat and whisk constantly. When it bubbles, cook 1 minute while whisking.
Temper yolks: Whisk egg yolks in a bowl. Slowly whisk in about ½ cup hot mixture. Pour yolk mixture back into saucepan.
Finish filling: Cook 2 minutes, whisking. Remove from heat and stir in lemon juice, zest, and butter.
Fill the crust: Pour hot lemon filling into the baked crust and smooth the top.
Make the meringue: Beat egg whites and cream of tartar until foamy, then to soft peaks. Add sugar 1 tablespoon at a time while beating. Continue until stiff peaks form. Beat in vanilla.
Top the pie: Spoon meringue over hot filling, sealing to the crust edge. Swirl into peaks with a spoon.
Bake: Lower oven to 350°F and bake 12 to 15 minutes, until lightly golden.
Cool and chill: Cool at room temperature 1 hour, then refrigerate at least 4 hours before slicing.