Preheat oven to 350°F. Grease only the bottom of an 8-inch square baking dish.
Add milk to a small saucepot and heat over medium heat. Once the milk begins to simmer, remove from heat, and add hojicha tea leaves. Steep for 30 minutes.
Strain the tea leaves, squeezing as much liquid as possible. Set aside ¼ cup of the infused milk for the cake batter. Measure the remaining milk, you should have about ½ cup. If needed, add a splash of plain milk to reach ½ cup. Add evaporated milk and sweetened condensed milk to the ½ cup infused milk, whisking until well combined. Set aside.
Make the cake batter. Sift all-purpose flour, baking powder, and salt into a medium bowl. Set aside.
In a large bowl, beat egg yolks with 6 tablespoons (75 grams) granulated sugar until the mixture is pale yellow and nearly doubled in volume, about 3–4 minutes. Add vanilla extract and the reserved ¼ cup of hojicha-infused milk, mixing until well combined. Add the sifted flour mixture, stirring just until incorporated.
In a separate large bowl, whip large egg whites until soft peaks form. Gradually add remaining 2 tablespoons granulated sugar while continuing to beat. Whip until stiff peaks form.
Add ⅓ of the whipped egg whites to the cake batter and stir to loosen. Gently fold in the remaining egg whites in two additions until just combined. Pour batter into the prepared pan and bake for 18–20 minutes or until a toothpick inserted in the center comes out clean. Let cool completely in the pan.
Prick the entire surface evenly with a fork. Slowly pour the hojicha milk mixture over the cake in stages, tilting the pan to coax the liquid into the corners and edges. Cover and refrigerate for at least 1 hour or overnight for best results.
Make white chocolate brown sugar whipped cream. Melt 2 ounces white chocolate gently in the microwave in 20-second intervals, stirring until smooth. Let cool to room temperature.
In a large bowl, whip heavy cream until soft peaks begin to form. Add brown sugar and continue whipping. Stream in the cooled melted white chocolate and whip until stiff peaks form. Spread whipped cream evenly over the chilled cake. Cut into 9 squares and serve cold.
Notes
You can infuse the milk the day before and chill it in the refrigerator until ready to use.