Stir half-and-half, coconut milk, eggs, 3/4 cup sugar, cornstarch, and salt together in a saucepan; stirring constantly, slowly bring to a boil over low heat and cook until thick, about 30 minutes. Remove saucepan from heat; fold 3/4 cup coconut into the mixture with the vanilla extract. Pour the coconut mixture into the baked pie crust.
Beat egg whites in a glass or metal bowl until foamy. Gradually add cream of tartar and 6 tablespoons white sugar, continuing to beat until soft peaks form. Lift your beater or whisk straight up: the egg whites will form soft mounds rather than a sharp peak. Spread egg white mixture over the pie. Sprinkle 1/2 cup coconut over the pie.
Bake in preheated oven until the top is golden brown, 12 to 15 minutes. Move to a wire rack to cool until completely cooled to the touch, about 1 hour. Refrigerate at least 3 hours before serving.