In a small pot, whisk ⅔ cup heavy cream and white chocolate over low heat until melted.
Transfer the white chocolate mixture to the bowl of a stand mixer and refrigerate for at least 15 minutes or until cool to the touch.
In the meantime, whisk to combine the boiling water with 1 tablespoon granulated sugar and 2 teaspoons matcha green tea powder. Set aside.
Stem and dice 4 large or 5 small strawberries. Stir to combine with remaining 1 tablespoon sugar and the lemon juice. Set aside.
Thinly slice 4 or 5 strawberries, reserving at least 3 strawberries for garnishing, and use the sliced strawberries to line 6 12-ounce tumblers. Set aside.
Cut the ladyfingers into small pieces (about ¾-inch). Set aside.
To the cooled white chocolate mixture, add the remaining 1 ⅓ cups heavy cream, kosher salt, and vanilla or rum. Use a whisk attachment to whip to soft peaks.
Add the mascarpone and whip to stiff peaks.
Transfer to a piping bag fitted with a medium round tip.
Pipe a layer of mascarpone cream into the bottom of each glass.
Top with 4 or 5 pieces of ladyfinger cookies.
Brush or drizzle ladyfingers generously with the green tea mixture.
Top with an additional layer of mascarpone cream.
Top evenly with the diced strawberry mixture.
Top with a final layer of ladyfingers, and brush or drizzle with green tea mixture.
Pipe mounds of cream in a ring shape in each glass.
Sift the remaining 2 tablespoons of matcha powder over the cream.
Halve the remaining strawberries, and place one half into the center of each glass.
Serve immediately or store in the refrigerator until ready to serve.