In a large overproof skillet, set over medium heat, melt the butter, with a drizzle of oil. Saut the onions until they are soft and golden. Transfer the slightly caramelized onions to an 8 or 9" round cake pan or pie plate that has been greased.
In a medium bowl, combine the flour, baking powder, and salt. In a small bowl, stir together the milk, oil, and egg. Add the milk mixture to the flour mixture and stir until just blended.
Spread the batter over the onions and bake for 35-40 minutes, until pale golden around the edges, cracked on top, and springy to the touch.