In a medium bowl, whisk together the brown sugar and hojicha powder. Gradually pour in the hot water while whisking continuously to ensure a completely smooth mixture. Stir in the dark rum if using, and let the syrup cool down completely.
Add the room-temperature mascarpone to a medium bowl. Smooth it gently using a rubber spatula just until pliable. Crucial: Do not over-mix, or the high fat content may cause the cheese to break and split.
Create a double boiler by setting a heatproof bowl over a pot of gently simmering water (ensure the bottom of the bowl does not touch the water). Whisk the egg yolks and sugar continuously over the steam until the mixture expands, thickens slightly, and turns a light yellow color. Remove from heat immediately to prevent scrambling.
Slowly pour the warm egg mixture into the softened mascarpone and whisk gently just until smooth and fully incorporated.
Transfer the bowl to the refrigerator to cool while you whip the cream.
In a separate, cold bowl, pour the chilled heavy cream. Use an electric hand mixer or stand mixer to whip the cream until soft, pillowy peaks appear.
Retrieve the mascarpone mixture from the refrigerator. Using a rubber spatula, gently fold the whipped cream into the cheese base in two separate additions to keep the texture light and airy.
Briefly dip both sides of the ladyfingers into the cooled hojicha syrup—moist, but not soggy. Arrange them in a single, tight layer at the bottom of a 5x7-inch dish, leaving no gaps.
Pour the mascarpone cream mixture over the layer of dipped ladyfingers.
Smooth out the surface completely flat using an offset spatula.
Use a fine mesh strainer to generously dust the entire top with pure hojicha powder. Cover and chill in the refrigerator for at least 3 hours (or overnight to allow the flavors to deepen).
Before serving, decorate with non-melt powder sugar if desired.