Dissolve the salt in the water. Using the dough hook, drizzle the salted water and cream into the flour. Shape into a ball, roll out into a rectangle, and let rest in the refrigerator. Roll out the dough and insert the butter sheet. Seal up the dough parcel and give it its turns.
Stir the rum and vanilla extract into the pastry cream, then stir in the melted gelatine mass. Whip the cream until stiff, then gently fold it into the pastry cream.
Rehydrate the gelatine in the cold water for at least 20 minutes. Melt in the microwave, then set aside in the refrigerator.
Prepare a dark caramel with all the ingredients. Pour onto a Silpat mat and let cool. Grind in a food processor. Store in an airtight container.
Heat the cream, milk, and glucose (1). Prepare a dark caramel with the glucose (2) and the sugar (approximately 195°C). Deglaze with the hot cream mixture. Reheat to 108°C. Add the fleur de sel and cream cheese. At 40°C, add the butter and blend with an immersion blender. Refrigerate overnight.
Give the puff pastry dough 5 single turns, letting it rest between turns. Roll out to a thickness of 3 mm. Cut into 60 x 40 cm rectangles (approximately 850 g). Let rest in the refrigerator for at least 4 hours (ideally overnight).
Using a cutter, cut the dough lengthwise into 20 cm long strips, then cut the strips into 3.5 cm wide rectangles (approximately 30 g).
Place on a baking tray lined with paper, place 2.5 cm high blocks on the tray, and cover with another baking tray. Bake in a 170°C convection oven for approximately 50 minutes or in a 180°C deck oven for approximately 1 hour.
Remove from the oven and cut 20 rectangles in half lengthwise using a serrated knife (so that the air cells are visible). Sprinkle the air cell side of the sliced pastry with the ground opaline. Do the same with the sides of the puff pastry bars and caramelize both in a 170°C oven for approximately 10 minutes. Let cool.
Turn the caramelized puff pastry bars over (bottom side up). Poke 3 holes in them using a small plain nozzle. Fill each with 20 g of pastry cream. Pipe 2 lines of vanilla diplomat cream on top using a plain 14 mm nozzle (approximately 40 g). Using an 8 mm nozzle, pipe a line of cream cheese caramel between the two lines of diplomat cream (approximately 10 g). Top with a slice of carmelized puff pastry.