Spray an 8-inch square baking pan with non-stick cooking spray.
Heat the olive oil in a skillet over medium-low heat; add the sweet onions and cook for 7 to 10 minutes, until light golden brown, stirring frequently. Set aside.
In a large bowl, combine the flour, cornmeal, baking powder, and pepper.
In another bowl, whisk the milk with the egg white. Add the cooked onions and blend well.
Add the onion mixture to the dry ingredients, stirring just until blended.
Spread the batter in the prepared pan.
Bake until the sides begin to pull away from the pan, about 20 minutes.
Cool before loosening the sides and turning out of the pan.