Chocolate pie is topped with fluffy peaks of meringue.
On a lightly floured surface, roll out 1 disk of dough to 1/8 inch thick. Cut into a 12-inch round. Fit into a 9-inch pie plate. Trim edges so that there is a 1-inch overhang. Fold under, and crimp with your fingers. Refrigerate for 1 hour.
Preheat oven to 425 degrees. Prick bottom of crust all over with a fork. Freeze 15 minutes. Line with parchment, and fill with pie weights or dried beans. Bake until edges are just golden, about 15 minutes. Remove weights and parchment. Return to oven, and bake until center is golden brown, about 15 minutes more. Let cool completely on a wire rack.
Whisk 1 cup sugar, the flour, and cocoa. Gradually whisk in 1/2 cup milk until smooth and thick. Whisk in egg yolks.
Heat butter, salt, and remaining 1 1/2 cups milk in a large saucepan over medium-high heat, stirring until butter has melted. Add about 1/4 cup butter mixture to the cocoa mixture, and whisk until smooth. Add cocoa-butter mixture to pan, and cook, whisking constantly, until thickened and beginning to bubble, about 1 minute. Remove from heat, and whisk in vanilla. Pour through a fine sieve into cooled piecrust. Let cool completely. Refrigerate for 1 hour.
Preheat broiler. Put egg whites, remaining 2/3 cup sugar, and the cream of tartar into a heatproof bowl set over a pan of simmering water. Whisk until sugar has dissolved and mixture reaches 160 degrees. Remove from heat. Beat on medium-low speed for 5 minutes. Raise speed, and beat until stiff, glossy peaks form, about 4 minutes. Spoon onto pie, making sure meringue touches crust. Broil until browned, 30 seconds to 1 minute.