In a medium saucepan, whisk together sugar (reserving a small portion), cornstarch, salt, lemon zest, and cold water. Cook over medium heat, whisking constantly, until mixture thickens and bubbles—about 5–7 minutes.

Remove from heat; stir in lemon juice and butter. Temper the egg yolks by slowly whisking in a small amount of the hot mixture, then pour yolk mixture back into the saucepan. Return to low heat, stirring until thick and glossy. Strain if needed for a silky finish.

Immediately pour the hot lemon filling into the cooled pre‑baked crust. Cover with plastic wrap directly on the custard surface to prevent skin formation, then let sit a few minutes while preparing meringue.

Preheat oven to 375 °F (190 °C). In a clean bowl, beat egg whites with cream of tartar until foamy. Gradually add the reserved sugar and vanilla, beating until stiff, glossy peaks form.

Spread the meringue evenly over the still‑warm lemon filling, sealing all the way to the crust edges to prevent weeping. Create decorative peaks with the back of a spoon.

Bake on a low rack until the meringue is set and lightly golden—about 5–7 minutes. Watch carefully to avoid over‑browning.

Let the pie cool on counter for 30–60 minutes before refrigerating for at least 2 hours to let the filling set fully.