Preheat the oven to 425 degrees F. Line 4 sheet pans with parchment paper.
Crack the egg into a small bowl, then add 1 tablespoon water and beat until well mixed. Pour half into a separate small bowl. Add a few drops of red food coloring to the egg in one bowl and a few drops of yellow to the other.
Unfold the puff pastry sheets and cut each into 3 rectangles, using the folded lines as a guide, for a total of 12 rectangles. Place 3 on each of the prepared sheet pans, leaving 2 to 3 inches in between each.
Top each of two pans of puff pastry with a second piece of parchment and place a second sheet pan on top of the parchment paper. Bake for 10 minutes, then remove the top sheet pans and top pieces of parchment. Return to the oven and bake until puffed and golden brown on the bottom, an additional 8 to 10 minutes. Let cool completely.
Top the remaining two pans of unbaked puff pastry with parchment and sheet pans and bake for 10 minutes. Remove the top sheet pans and parchment. Brush these partially-baked rectangles with red egg wash on one end and yellow on the other, overlapping the two in the middle to create an orange section. Return to the oven to finish the baking, another 8 to 10 minutes. Let cool completely.
Make the filling in two batches so that it will fit in the mixer. Add half the cream cheese and half the powdered sugar to a stand mixer fitted with the whisk attachment and beat until light. Add 3 cups heavy cream and beat to stiff peaks. Add half the chocolate hazelnut spread, then fold in using a rubber spatula until no streaks remain. Transfer to a piping bag or large resealable plastic bag fitted with a large closed-star tip and refrigerate until ready to use. Repeat the process with the second half of the filling ingredients, leaving this portion in the bowl. Refrigerate until ready to use.
Split each of the puff pastry rectangles open horizontally using a serrated knife. Line up 6 of the bottom half puff pastry rectangles end-to-end down a long platter, using a dot of filling to secure to the platter if necessary. Pipe an even layer of filling down the puff pastry line. Top with 6 more puff pastry rectangles and repeat with filling and puff pastry twice more, refilling the piping bag as needed and ending with the colored puff pastry, lining them up with red ends touching. (See Cook's Note.)
Drizzle the melted chocolate over the top of the puff pastry and top with broken pieces of Hazelnut Brittle.
Line a baking sheet with a silicone baking mat.
Add the granulated sugar, corn syrup and 1 cup water to a medium saucepan and stir to combine. Cook over medium-high heat until the syrup begins to turn golden brown, 10 to 15 minutes. Continue to cook, swirling the pan gently, until the mixture is a deep amber color.
Remove the saucepan from the heat and stir in the nuts and salt. Pour immediately onto the prepared baking sheet. Spread into an even layer and let cool completely, then break into small pieces.
To make this in advance, stack and layer each separately and refrigerate. When ready to serve, place each napoleon end-to-end down a long platter, using a small amount of filling to adhere to the platter if necessary.