Prep the pie shell. Preheat the oven to 450℉. Then, roll out your pie crust into a 9-inch pie plate, pressing it firmly into the edges. Prick the base with a fork to prevent bubbling while baking. Set aside.
Prepare the custard base. Whisk together the cornstarch and 4 tablespoons of milk in a small bowl until smooth. Then, add the egg yolks and whole egg, whisking until well combined. Set aside. Next, in a medium saucepan, combine the remaining milk and granulated sugar. Bring this mixture to a gentle boil over medium-high heat, stirring occasionally. Once it reaches a boil, remove from the heat.
Temper the eggs. Slowly pour about ¼ cup of the hot milk into the cornstarch-egg mixture, whisking constantly to prevent curdling. Then, pour the tempered egg mixture into the saucepan with the remaining hot milk.
Cook the custard and add the chocolate. Return the pan to medium-high heat and cook, stirring constantly, until the mixture thickens to a custard-like consistency, about 5 minutes. Then, remove from heat and stir in the butter and vanilla extract until melted and smooth. Next, add the chocolate chips and stir until fully melted and incorporated.
Fill the pie shell. Pour the warm chocolate custard filling immediately into the prepared pie shell, spreading it evenly. Set aside to cool it slightly while you prepare the meringue.
Make the meringue. In a clean, medium-sized bowl, add the egg whites and cream of tartar. Using a handheld electric mixer on medium speed, beat the egg whites until soft peaks form. Then, slowly add the granulated sugar a little at a time, and increase the mixer speed to high. Continue beating until the meringue is glossy and holds stiff peaks. (Avoid overmixing, as this can cause the meringue to release liquid.)
Top and bake the pie. Preheat the oven to 450℉ if it has cooled. Use a rubber spatula to spread the meringue over the chocolate filling, ensuring it touches and seals the edges of the crust to prevent shrinking. Place the pie in the oven and bake for 3-5 minutes, watching closely to prevent burning. The meringue should turn a light golden brown.
Cool and serve. Remove the pie from the oven and let it cool at room temperature for at least 2 hours before slicing. This helps the filling set fully. Enjoy your slice!