Preheat oven to 350 degrees F (175 degrees C). Grease a 9-inch Bundt pan or a 9×13 inch baking pan.
In a large bowl, mix together the butter, sugar, eggs, vanilla and milk. Stir in the rice flour and baking powder. Pour the batter into the prepared pan. Drop red bean paste by scant teaspoonfuls onto the top of the cake. If spoonfuls are too big, the filling will sink to the bottom.
Bake for 1 hour and 10 minutes in the preheated oven, or until cake springs back when lightly touched. If using a Bundt pan, invert the cake onto a serving plate. Cake must be completely cooled before unmolding from Bundt pan, or it will be too soft to hold its shape. Serve small slices of this very rich cake at room temperature or slightly warmed.