Whip: In the bowl of a stand mixer fitted with the whisk attachment, combine the cold heavy cream, milk, instant pudding mix, sugar, and vanilla. Whip on medium-high until thick and fluffy, about 2 to 3 minutes.
Add the Sour Cream: Add the sour cream and whip briefly, just until smooth and combined. Don't overwhip.
Layer the cake
Dip: Pour the cooled coffee into a shallow dish. Dip each biscuit for 1 to 2 seconds on each side. Don't soak them, or they'll fall apart.
First Layer: Arrange a single layer of dipped biscuits in the bottom of a 9x9 inch pan.
Cream: Spread ⅓ of the pudding cream evenly over the biscuits with an offset spatula.
Repeat: Add two more layers of dipped biscuits and cream, finishing with a smooth layer of cream on top.
Make the ganache
Heat: Warm the heavy cream in a small saucepan or the microwave until it's steaming and just starting to bubble at the edges.
Melt: Pour the hot cream over the chopped chocolate. Let it sit for 2 minutes, then stir gently from the center out until smooth and glossy.
Finish and chill
Let the ganache cool for 5 to 10 minutes so it's still pourable but no longer hot. Pour it over the top layer of biscuits and spread it into an even layer.
Cover and refrigerate for at least 6 hours, or ideally overnight, until the biscuits are soft and the ganache is set.
Notes
Instant Pudding: Use instant vanilla pudding mix, not cook-and-serve, or the cream won’t set.
Keep It Cold: Use very cold heavy cream and milk so the cream whips into stiff, stable peaks.
Quick Dip: Dip the biscuits for just 1 to 2 seconds per side. They keep softening in the fridge as the cake chills.
Even Layers: Divide the cream into 3 equal portions so each layer is the same thickness.
Ganache Temperature: Let the ganache cool for 5 to 10 minutes before pouring, so it doesn’t melt the top layer of cream.
Chill Time: Refrigerate for at least 6 hours, or ideally overnight, so the biscuits turn soft and cake-like and the slices hold their shape.
Clean Slices: Use a sharp knife dipped in hot water and wiped dry between each cut.
Substitute:Graham crackers can replace the petit beurre biscuits.