01 - Preheat oven to 350°F (175°C). Line an 8-inch square baking pan with parchment paper.
02 - Melt butter and chopped chocolate together in a heatproof bowl set over simmering water, stirring until smooth.
03 - Whisk granulated sugar into the chocolate mixture, followed by eggs one at a time and vanilla extract.
04 - Sift all-purpose flour, matcha powder, and salt into the bowl; gently stir until just combined.
05 - Fold white miso paste into the batter, leaving visible streaks for a marbled finish.
06 - Pour batter into prepared pan. Bake for 20 to 25 minutes, until set but retaining a fudgy texture. Allow to cool completely before slicing.
07 - Beat mascarpone cheese, heavy cream, sugar, and vanilla extract with an electric mixer until thick and smooth.
08 - Quickly immerse ladyfinger biscuits into cooled chai tea and arrange in serving cups or glasses.
09 - Spread the mascarpone mixture over the ladyfingers, dusting the surface with ground cinnamon, ground cardamom, and cocoa powder.
10 - Refrigerate at least 2 hours before serving to allow flavors to meld.
11 - Combine chocolate cookie crumbs with melted butter. Press mixture firmly into a lined 8-inch square pan.
12 - Beat softened cream cheese with sugar until smooth. Incorporate eggs individually, then add black sesame paste, vanilla extract, and a pinch of salt.
13 - Pour cheesecake filling over the crust and smooth the top. Bake at 325°F (160°C) for 25 to 30 minutes or until set.
14 - Allow bars to cool to room temperature, then chill in the refrigerator at least 2 hours before cutting into portions.