Preheat your oven to 350°F. Place your pre-baked pie crust shell on a flat baking sheet and set it aside.
Separate your eggs carefully while they are cold, placing the whites into a completely clean, grease-free glass or metal mixing bowl and the yolks into a separate medium bowl. Let them sit for 20 minutes to reach room temperature.
In a large, heavy-bottomed saucepan, whisk together 1 cup of the granulated sugar, the cocoa powder, cornstarch, and salt until completely blended.
Slowly pour the whole milk into the dry chocolate mix, whisking constantly to ensure no floury pockets remain at the bottom of the pan.
Place the saucepan over medium heat. Stir continuously with a wooden spoon or silicone spatula, scraping the bottom corners often, for 6 to 8 minutes until the mixture bubbles softly and thickens into a heavy pudding consistency. Remove from the burner.
The Tempering Trick: Whisk your 4 egg yolks vigorously until smooth. Slowly drizzle exactly 1 cup of the hot chocolate pudding baseline into the egg yolks while whisking the eggs with your other hand. This raises the temperature of the yolks gently so they don't scramble.
Pour the warmed egg yolk mixture back into the main saucepan with the remaining chocolate pudding. Return the pan to medium-low heat and cook for an additional 2 minutes, stirring non-stop until the custard turns glossy and thick.
Remove the pan from the heat entirely. Stir in the 2 tablespoons of butter and 1 teaspoon of the vanilla extract until melted and incorporated. Keep the saucepan covered so the custard stays hot.
Quickly switch to your egg whites. Add the cream of tartar to the whites and whip with an electric mixer on medium-high speed until soft peaks form.
With the mixer running, add the remaining ½ cup of sugar one tablespoon at a time, followed by the remaining ½ teaspoon of vanilla. Turn the mixer to high and whip until the whites turn glossy and hold stiff, upright peaks when the beaters are lifted.
Pour the hot chocolate custard baseline directly into your pre-baked pie shell, smoothing it into an even layer.
Immediately spoon the whipped meringue topping over the hot custard. Use a flexible spatula to spread the meringue all the way to the absolute edges of the crust, sealing the borders completely to lock in the steam. Swirl the top with the back of a spoon to create beautiful decorative peaks.
Place the pie into the oven at 350°F for 12 to 15 minutes. Watch it closely; it is finished the exact moment the peaks of the meringue take on a gorgeous, toasted golden-brown color.
Remove the pie from the oven and let it cool flat on a wire rack at room temperature for 1 hour. Transfer it to the refrigerator to chill uncovered for at least 3 to 4 hours to allow the chocolate custard to set perfectly before slicing.