Make the cake.  Preheat oven to 350 degrees F/ 325 degrees F convection.  Oil a 9 by 13 inch pan.

In a large bowl, whisk together flour, sugar, carob or cocoa, baking soda, baking powder, and espresso powder until combined.  Whisk in the eggs, milk, coffee, vanilla, and oil until the batter comes together and is mostly lump free.

Pour batter into the prepared pan and bake 40-50 minutes until puffed and a toothpick inserted in the center comes out clean or with a few moist crumbs.  Cool completely in the pan.

Make the pudding.  In a medium bowl, whisk together the egg yolks and tapioca starch.  In a medium saucepan, whisk together the cream, milk, sugar, and carob.  Place over medium heat and bring to a simmer, stirring frequently.

Once the cream mixture is simmering, remove it from the heat and slowly drizzle about 1/3 of it into the egg yolks while whisking.  At this point, pour the egg mixture into the pot.  Whisking constantly, place back over the heat and cook until the pudding is thickened about bubbling, no more than 5 minutes.

Remove from the heat, pour into a bowl and whisk in the vanilla and coconut butter.  Cover with plastic wrap directly on the pudding and refrigerate until totally chilled, up to 24 hours before assembling the cake.

Make the crumbs.  Preheat the oven to 325 degrees F.  Line a baking sheet with parchment.  In a medium bowl, stir together the flours, carob or cocoa, sugar, and espresso until combined.  Stir in the oil until clumps form.  Spread in an even layer on the tray and bake for about 30 minutes, stirring every 8-10 until slightly firm.  Crumbs will continue to harden as they cool.  Cool completely on the tray.  Crumbs may be made up to 1 week ahead and stored in an airtight container at room temperature.

Assemble the cake.  Using a serrated knife, slice off the domed top of the cake, crumble it, and combine with the crumb topping.

Spread the pudding in an even layer on top and then sprinkle with the crumbs.  Serve immediately or cover with plastic and store in the refrigerator for up to 4 days.