Prepare the Matcha Dipping Liquid: In a bowl, whisk together the hot water, 3 Tbsp matcha powder, and 1/4 cup sugar until dissolved. Stir in the optional rum/liqueur. Set aside to cool completely to room temperature.

Create the Sabayon Base: In a heatproof bowl set over a saucepan of simmering water (creating a double boiler), whisk the egg yolks and 1/2 cup sugar continuously until the mixture is pale yellow, thick, and reaches 160°F (71°C). Remove from heat and whisk vigorously until cooled down slightly.

Make the Mascarpone Cream: In a separate large bowl, whip the cold heavy cream until stiff peaks form. In another bowl, gently fold the mascarpone cheese into the cooled sabayon base until smooth. Gently fold the whipped cream into the mascarpone mixture in two additions until just combined, being careful not to deflate the cream.

Assemble the Tiramisu: Quickly dip each ladyfinger, one by one, into the cooled matcha liquid—do not over-soak. Arrange a single layer of dipped ladyfingers in the bottom of an 8x8 inch baking dish or a comparable serving dish.

Layer and Chill: Spread half of the mascarpone cream evenly over the layer of ladyfingers. Create a second layer of dipped ladyfingers, followed by the remaining mascarpone cream. Cover the dish tightly with plastic wrap and refrigerate for at least 3 hours, or preferably overnight, to allow the flavors to meld and set.

Serve: Before serving, use a fine-mesh sieve to generously dust the top layer of the chilled tiramisu with the remaining 1 tsp of matcha powder.