Preheat oven to 350 degrees.
Cream in an electric mixer soft butter, sugar, and vanilla.
Mix in milk, flour, cornstarch. Beat in eggs one by one.
Stir in baking powder, rum, and salt.
Spoon in an 8-inch buttered round mold. Peel and slice 3 apples.
Stick slices in batter.
Bake 35 to 40 minutes.