Whisk the flour, sugar, baking powder, baking soda and salt together.
In a separate bowl, whisk the egg, milk and melted butter until smooth, then combine with the dry ingredients just until no streaks of flour remain. Let the batter rest 10 minutes.
Heat a bungeoppang mold (or a fish-shaped waffle iron) over medium-low heat and brush both sides lightly with oil.
Spoon a thin layer of batter into one side of the mold, just enough to cover the base.
Add a generous line of red bean paste down the center, running it close to both the head and tail ends — this is the step people skip, and skipping it is why the ends of a bungeoppang so often come out with no filling at all.
Spoon a little more batter over the top to cover the paste, then close the mold.
Cook 2 to 3 minutes per side, checking and flipping the whole mold, until both sides are evenly golden brown.
Open carefully and let each piece sit a minute before eating — the filling holds heat much longer than the shell does.