1. Infuse whole milk with genmaicha tea by refrigerating for up to 24 hours. Strain the tea leaves out to yield about 275g of flavored milk.
2. Mix the infused milk with coconut milk and condensed milk, adjusting sweetness to taste.
3. Preheat the oven to 350°F (175°C). Butter an 8-inch square baking pan and line the base with parchment paper.
4. In a mixer, beat eggs until frothy, then gradually add sugar. Whip until the mixture is light and forms a ribbon that holds its shape.
5. Sift together flour, baking powder, and salt, and gradually fold into the egg mixture to avoid lumps.
6. Pour the batter into the prepared pan, smooth the top, and bake for about 20 minutes or until a skewer inserted in the center comes out clean.
7. Let the cake cool. Poke holes evenly across the cake and pour the milk mixture slowly over it, making sure it absorbs completely. Chill thoroughly.
8. Before serving, spread whipped cream over the cake, dust with matcha powder if desired, and add fruit toppings. Serve with a sharp serrated knife for clean slices.