Combine cake flour and baking powder, and sift together a couple of times. Make Anko bean paste into 10 tablespoon-size balls. Spread 1/2 cup sugar thinly on a plate or baking sheet. Set all aside.
In a large bowl, put soft butter and sugar, and whisk well. Add lightly beaten egg to butter mixture in 3 parts. Then add milk and vanilla and whisk. Add flour mixture, and mix with a wooden spatula or spoon until the dough becomes uniform. If it's too sticky, let rest in the fridge for 30 minutes.
Divide the dough into 10 pieces, and form balls. Flatten the dough into 3" (7.5 cm) rounds making the center thicker and the edges thinner. Take an Anko ball, put it in the center of the dough, and wrap it with the dough completely.
Heat deep-frying oil at medium low temperature. Cook the doughnut balls until golden brown turning frequently. Take care not to burn the surface of the dough.
While doughnuts are still hot, coat with sugar.
