Preheat oven to 325 F. Prepare a 9x5 loaf pan by greasing it lightly with butter. In a bowl, sift together the cake flour, baking powder, and salt. Set aside.
In another bowl, stir together the yolks, ube flavoring, 1/4 cup sugar, milk, water, melted butter and vegetable oil. Use an electric mixer and beat the ingredients at low speed just until combined. Add the dry ingredients and continue beating until the batter is smooth. This should take about 2-3 minutes. Set aside.
In another bowl, use a clean beater and beat the egg whites using medium speed until frothy. Increase the speed and add the cream of tartar. Continue to beat until soft peaks are formed. Gradually add 1/2 cup of sugar until firm peaks are formed.
Fold the egg whites into the yolk batter using a rubber spatula, gently adding 1/3 of the meringue at a time. The batter should be uniform in color. Pour batter into the prepared loaf pan and bake at 325 F for 35-40 minutes.
Let cool slightly before removing from the pan. Transfer to a serving plate and brush with melted butter, sprinkle with sugar and grated cheese.