1Preheat the oven to 350°F and grease a large ramekin with butter.
2In a medium bowl, mix together the softened butter and oil then mix in the sugar until pale and slightly fluffy.
3Mix in the egg white, milk, and vanilla extract until combined.
4Fold in the flour, baking powder, and salt with a rubber spatula.
5Pour the batter into the greased ramekin.
6Bake for 22-27 minutes until it is golden on top, a toothpick comes out with just moist crumbs, and if you gently press the top of the cake it slightly bounces back.
7Allow the cake to cool for 5-10 minutes before removing from ramekin.
8While the cake cools completely, make the frosting. Stir together the butter and milk with a fork in a small bowl.
9Mix in the powdered sugar and vanilla.
10Spread the frosting on top of the cooled cake and enjoy!