Make the Chocolate Filling:

1. Pre-bake the Pie Crust:
   Bake the pie crust as directed on the package or recipe. If there is a range of time, bake for the shorter time, as it will go back in the oven with the filling and meringue. Set aside to cool.
2. Prepare the Filling:
   Separate the 3 eggs. Set the egg whites aside for the meringue.
   In a large saucepan, combine the unsweetened chocolate, ¼ cup sugar, and water. Cook over medium heat until the chocolate melts and the mixture is smooth, stirring occasionally.
   Add the flour, remaining ½ cup of sugar, salt, and milk to the saucepan, whisking until the mixture is smooth. Cook over medium heat, stirring constantly for 12-15 minutes, until the mixture thickens and becomes a deep brown color.
3. Temper the Egg Yolks:
   In a small bowl, whisk the egg yolks until smooth. Gradually add two ladles of the hot chocolate mixture, one at a time, into the yolks, whisking quickly to combine and prevent curdling.
   Pour the tempered egg yolks back into the saucepan with the chocolate mixture, stirring constantly until fully combined.
4. Finish the Filling:
   Add the vanilla extract and butter to the saucepan, stirring until the mixture is thick and smooth.
   Pour the chocolate filling into the pre-baked pie crust, spreading it evenly. Set aside while preparing the meringue.

Make the Meringue Topping:

1. Beat the Egg Whites:
   In a clean mixing bowl, beat the reserved egg whites until they start to become foamy and bubbly.
   Add the cream of tartar and continue mixing until soft peaks form.
2. Add the Sugar:
   Gradually add the 3 Tablespoons of sugar, 1 tablespoon at a time, and continue beating until the egg whites hold stiff, glossy peaks.
3. Assemble and Bake:
   Gently spread the meringue over the chocolate filling, making sure to extend it to the edges and slightly over the crust to seal in the filling.
   Bake at 375°F (or according to the temperature specified for the pie crust) for about 10 minutes, or until the meringue is lightly browned on top.
4. Cool and Serve:
   Remove the pie from the oven and allow it to cool completely at room temperature. Once cooled, refrigerate the pie for a few hours to let the filling set before serving.