To make the matcha soak: Sift matcha into a medium bowl and slowly whisk in hot water, breaking up clumps until all water has been combined and no lumps remain.
To make the cream: Add mascarpone cheese, sugar, egg yolks, rum, heavy cream and salt into the bowl of a mixer. Mix with whisk attachment on medium-high speed until medium peak appears, about 5-7 minutes. Be careful to not overmix, or mascarpone will separate.
To assemble: Prepare a 9x5” baking dish or a tupperware (This is flexible and you can use a different size container as well). Spread a thin, even layer of cream onto the bottom of the baking dish.
Dip ladyfingers, one at a time, into matcha mixture, rolling over 2 to 3 times to saturate. The ladyfingers should start to soften but not become soggy enough to fall apart. (*Footnote 2) Then place them over the cream, snugly, next to each other. Repeat until the first layer of baking dish is filled with ladyfingers.
Add about 1/2" of cream mixture on top of the ladyfingers and spread evenly to cover completely. Repeat with the next layer of ladyfingers and matcha, covering with the remaining cream. Smooth the top layer of cream as evenly as possible.
Dust with a thin layer of matcha using a fine mesh strainer.
Refrigerate at least 2 hours and ideally overnight before serving.
Notes
The ideal temperature for making matcha is around 80°C (176°F). Hotter water draws out the bitterness of the matcha, and a lower temperature water makes a mellower tasting matcha.
I like the ladyfingers to have a little structure, so I prefer not to oversoak them. If you like a very moist texture, you can soak the ladyfingers a little longer. Just be careful, the ladyfingers will keep softening up once you place them onto the cream.