Heat oven to 350°F and grease and flour a 9-by-13-inch metal pan.
Whisk flour, baking powder and salt in a bowl.
Beat butter, oil and sugar until pale, then beat in eggs one at a time and add vanilla.
Mix in the flour mixture in three additions, alternating with 1 cup milk.
Spread batter evenly and bake for 28 to 32 minutes until a tester comes out clean; cool completely.
Beat frosting butter and cocoa, then add confectioners' sugar and 1/3 cup milk until soft and spreadable.
Frost the cake in the pan and cut into 20 squares.