Preheat oven to 375 degrees F (190 degrees C). Line a cake pan with parchment paper. Butter the paper and sprinkle with 1 teaspoon superfine sugar.
Bring a saucepan of water to a boil; pour into a large bowl.
Whisk 1/4 cup honey and milk together in a bowl until smooth.
Beat eggs with an electric mixer in a bowl placed over the hot water. Gradually add 1 1/3 cup superfine sugar; beat until smooth and mixture is warm. Remove bowl of egg mixture from the bowl of hot water and cool to room temperature, about 5 minutes. Return bowl of egg mixture to the hot water and continue beating. Repeat this process a few times until batter is foamy and thick.
Pour milk mixture into egg mixture and mix well using a spatula; stir in sifted flour until batter is mixed. Pour batter into the prepared cake pan.
Bake in the preheated oven until a toothpick inserted in the center of the cake comes out clean, about 50 minutes. Spread the remaining 1 tablespoon honey over the top of cake. Serve slices with sweet bean paste and ice cream, if desired.
