Line a baking sheet with parchment paper and preheat the oven to 340°F (170°C), convection if available.

To prepare the crumble, mix the butter, sugar, flour, cocoa, and vanilla paste in a stand mixer fitted with the paddle attachment until it forms coarse crumbs. Roll the mixture between two sheets of parchment to about ⅛ inch thick. Freeze until firm, then cut into 2½-inch/6 cm rounds. Keep frozen until ready to use.

For the choux pastry, combine water, milk, butter, sugar, and salt in a medium saucepan and bring to a full boil. Add the flour all at once and stir vigorously with a wooden spoon over medium heat until the dough pulls away from the pan and forms a smooth ball, about 2 minutes. Transfer to the bowl of a stand mixer fitted with the paddle attachment and mix on low speed for 2 minutes to cool slightly.

Add the eggs one at a time, allowing each to incorporate fully before adding the next. The dough should be glossy and pipeable, holding soft peaks. Transfer to a piping bag fitted with a large round tip. Pipe 2-inch/5 cm rounds onto the baking sheet, spacing them about 2 inches apart. Press a frozen crumble disc gently onto each puff.

Bake for 30 to 35 minutes, until golden brown and crisp. Do not open the oven door during baking. Cool completely on a wire rack.

To make the diplomat cream, heat the milk and vanilla paste in a saucepan over medium heat until steaming. In a separate bowl, whisk the sugar, cornstarch, and yolks until pale and smooth. Slowly whisk in a third of the hot milk to temper, then return the mixture to the saucepan. Cook over medium heat, whisking constantly, until thickened and bubbling, about 2 minutes.

Remove from heat, whisk in the butter, and transfer to a shallow container. Cover with plastic wrap pressed directly onto the surface and refrigerate until cold, at least 2 hours. Once chilled, whip the heavy cream to soft peaks and fold it gently into the pastry cream until smooth.

To make the ganache, bloom the gelatin by combining it with cold water and letting it sit for 10 minutes. Melt the white chocolate with the hot cream in a heatproof bowl set over a saucepan of simmering water, or in a microwave in 20-second bursts, stirring between each. Stir in the salt, vanilla, bloomed gelatin, and cold cream. Chill for at least 8 hours. When ready to use, whip until smooth and soft but able to hold shape.

To assemble, use a paring knife or piping tip to cut a small hole in the base of each puff. Pipe in the diplomat cream until full. Pipe a tall swirl of whipped ganache on top of each puff. Use a spoon to indent the ganache and add a small spoonful of black vanilla paste, if using.

Serve immediately or refrigerate for up to 6 hours.