Step 1: Ensure your 9-inch pie crust is pre-baked and completely cooled. Set aside.
Step 2: In a medium saucepan, whisk together the 1 cup sugar, 1/4 cup flour, and 1/2 cup cocoa powder. Gradually whisk in the 2 cups milk until smooth. Add the 3 egg yolks and 1/4 cup butter.
Step 3: Cook the mixture over medium heat, stirring constantly with a whisk, until it thickens and comes to a gentle boil. It should be thick enough to coat the back of a spoon. This typically takes 8-10 minutes. Remove from heat and stir in the 1 tsp vanilla extract.
Step 4: Pour the hot chocolate filling into the cooled, pre-baked pie crust. Smooth the top with a spoon or spatula. Set aside.
Step 5: For the Meringue: In a clean, dry mixing bowl, beat the 3 egg whites with the 1/4 tsp cream of tartar using an electric mixer on medium-high speed until soft peaks form.
Step 6: Gradually add the 1/2 cup granulated sugar, 1 tablespoon at a time, continuing to beat until stiff, glossy peaks form and the sugar is fully dissolved (about 3-5 minutes).
Step 7: Carefully spread the meringue over the warm chocolate filling, making sure to spread it all the way to the edges of the crust to seal it and prevent shrinkage. Create decorative peaks with the back of a spoon.
Step 8: Bake in a preheated oven at 350°F (175°C) for 10-15 minutes, or until the meringue is beautifully golden brown.
Step 9: Remove the pie from the oven and let it cool completely on a wire rack at room temperature for at least 2 hours. Then, refrigerate for at least 2-3 hours (or overnight) before slicing and serving. This ensures the filling is perfectly set.