In a medium saucepan, combine the 5 cups of half-and-half, 4 ounces of butter, and 1 cup of sugar. Heat over medium until the butter melts and the mixture is warm.
In a separate bowl, whisk together the 3 eggs, 1/4 cup of cornstarch, 1 teaspoon of vanilla extract, and 1/4 teaspoon of salt. Gradually add this mixture to the warm half-and-half mixture, whisking continuously to prevent curdling.
Continue to cook the mixture over medium heat, stirring constantly until it thickens (about 5-7 minutes). Once thickened, remove from heat and fold in the 1 cup of miniature marshmallows and 1 1/4 cups of flaked coconut. Allow the filling to cool slightly.
Place your 2 baked pie shells on a cooling rack. Pour the coconut filling evenly into the pie shells, smoothing the top with a spatula.
In a clean mixing bowl, beat the 1 1/4 cups of egg whites with 1 teaspoon of cream of tartar until soft peaks form. Gradually add 1 1/2 cups of sugar and continue beating until stiff, glossy peaks form.
Carefully spread the meringue over the coconut filling, making sure to seal the edges to prevent shrinking. You can create peaks and swirls for a decorative touch.
Bake the pie in a preheated oven at 350°F (175°C) for about 10-15 minutes, or until the meringue is lightly golden brown. Keep an eye on it to prevent over-browning.
Allow the pie to cool at room temperature before refrigerating for at least 2 hours. Slice and serve chilled.