Place the milk chocolate, dark chocolate, and heavy cream in a microwave-safe bowl and heat in short bursts, stirring between pulses, until smooth and glossy.

Pulse the Petit Beurre biscuits in a food processor to fine crumbs. Combine the crumbs with the melted chocolate mixture until evenly moistened, press firmly into the bottom of a 9-inch/22 cm springform pan, and freeze until the cream is ready.

In the bowl of a stand mixer fitted with the whisk, combine heavy cream, milk, and powdered sugar. Whip on medium speed until soft peaks form, then add 96 grams instant vanilla pudding mix and mix just until uniform and thickened.

Pour the cream over the chilled base and smooth with an offset spatula. Refrigerate for 1½ hours to set.

Release the cake from the pan, slice with a hot knife, and serve chilled.