Preheat oven to 375°F (190°C). Whisk flour and 1/2 tsp salt. Cut in butter until coarse crumbs form. Add ice water, 1 tbsp at a time, until dough holds together. Shape into a disk, chill 30 minutes. Roll out to a 12-inch circle, fit into a 9-inch pie plate, trim and crimp edges. Prick bottom, line with parchment and weights, blind-bake 20 minutes. Remove weights, bake 10-15 minutes more until dry and pale golden. Cool completely. Reduce oven to 325°F (160°C).

In a bowl, whisk granulated sugar, brown sugar, cocoa powder, cornstarch, and 1/4 tsp salt until no lumps remain.

In a saucepan, heat milk and cream over medium until steaming. Remove from heat, whisk in chocolate and espresso powder until smooth.

Add eggs to dry ingredients, whisk until thick. Slowly drizzle in about 1/2 cup warm chocolate milk, whisking constantly. Pour the egg mixture back into the saucepan. Cook over low heat, stirring, until custard thickens slightly and coats a spoon, 3-4 minutes. Remove from heat, stir in vanilla. Strain custard through a fine-mesh strainer into the cooled crust.

Place pie on a baking sheet. Bake at 325°F for 30-35 minutes, until edges are set and center jiggles slightly. Cool on a wire rack for 1 hour, then refrigerate at least 2 hours.

Slice with a hot knife and serve chilled. The custard should be dark and satiny, holding a clean wedge.