Pulse flour, sugar, and salt in a food processor 3 to 4 times or until combined. Add butter and shortening and pulse 10 to 12 times or until mixture resembles coarse meal. Drizzle 4 tablespoons ice water over mixture; pulse 5 to 6 times or until dough clumps together, adding up to 1 tablespoon water, 1 teaspoon at a time, if necessary. Gently shape dough into a flat disk. Wrap in plastic wrap, and chill for 30 minutes.

Preheat the oven to 400 degrees F (200 degrees C).

Roll dough into a 12-inch circle (about ⅛ inch thick) on a floured surface. Fit into a 9-inch pie plate; turn edges under and crimp. Prick the bottom and sides with a fork. Line pastry with parchment paper, and fill with pie weights or dried beans.

Bake in the preheated oven for 12 minutes. Remove pie weights and parchment paper and continue to bake until lightly browned and crisp, 10 to 12 minutes more. Transfer to a wire rack and cool while preparing filling.

Whisk together sugar, flour, cocoa powder, and salt in a large saucepan. Whisk together heavy cream, milk, and egg yolks in a medium bowl until completely blended. Gradually whisk egg mixture into sugar mixture.

Cook over medium heat, whisking constantly, just until mixture begins to boil, 6 to 8 minutes. Cook for 1 more minute, whisking constantly. Remove from heat and whisk in semisweet chocolate, bittersweet chocolate, butter, and vanilla until chocolate and butter have melted and mixture is completely smooth.

Spread filling in the cooled crust. Place plastic wrap directly on the warm filling and chill in the refrigerator until set, 8 to 24 hours.

Beat heavy cream and vanilla at medium-high speed with an electric mixer until foamy. Gradually add 3 tablespoons sugar, beating until soft peaks form.

Just before serving, top pie with whipped cream.