Preheat the oven to 375 degrees F (190 degrees C). Line a 15x10x1-inch jelly roll pan with waxed paper.
Combine flour and baking powder in a small bowl.
Beat egg yolks in a bowl using an electric mixer until light in color. Add 1/2 cup white sugar, water, green tea powder, and vanilla extract. Beat on low speed until well combined.
Beat egg whites in a small bowl using clean beaters until soft peaks form. Fold egg whites into the egg yolk mixture.
Sprinkle flour mixture over the egg mixture; fold until just combined. Spread batter evenly into the prepared pan.
Bake in the preheated oven until top is golden and cake springs back when lightly touched, about 12 minutes.
Mix cream cheese and coffee together in a separate bowl to make the filling. Sprinkle a piece of aluminum foil the size of the cake with confectioners' sugar.
Immediately loosen edges of cake from the jelly roll pan and turn cake out onto the sugared aluminum foil. Roll up foil and cake, starting from the cake's short end. Let cool to room temperature, at least 20 minutes.
Unroll cake and spread filling over the inside, within 1/2 inch of the edges. Roll up cake. Wrap in plastic wrap and refrigerate, about 30 minutes.
