Cut croissants in half, lengthwise to make 12 croissant halves. Place 4 of the bottoms on a baking sheet; shred half of the cheese overtop. Layer with 4 croissant tops and the remaining shredded cheese; top with the remaining 4 croissant.
In bowl, whisk eggs, cream and salt. Pour over croissant cheese towers.
Place a 9-inch baking pan overtop filled with warm water and bake for 1 hour. Remove the tray and continue baking until centre is hot, about 160°F.
Press and chill overnight. Cut into 12, 2 cm wide x 5 cm long rectangle portions.
In a skillet over medium-low heat, brown the Berskswell puddings all over; add birch sap and cook, spooning over towers until caramelized.
Stout Vinegar Gel
Combine vinegar, sugar and agar agar in a saucepan and bring to a boil over medium-high heat; whisk and cook for 1 minute. Strain through a fine-mesh sieve into a bowl. Let cool and set. Strain through a fine-mesh sieve, pressing with the back of a spoon into another bowl.
To serve, arrange two Berskwell puddings on each small plate. Pipe or spoon a large round of the stout vinegar gel beside the pudding then finely grate a heaping mound of Berkswell cheese on top using a microplane.