Preheat oven to 350 degrees. Butter baking dish and set aside.
Mix softened butter, both sugars, and peanut butter in a large mixing bowl. (You can use crunchy or smooth peanut butter.) Add the eggs and vanilla and combine thoroughly. Add the flour, oats, and baking powder, then mix well.
Press batter into the prepare baking dish. Bake for 15 minutes, or until a very light brown. (Don't overbake.) Let cool.
Peanut Butter Frosting
While the bars are baking, add 1/2 cup butter and 1/2 c. peanut butter to a large saucepan. Melt over medium heat, stirring until smooth, then remove from stove. Add 2-3 tablespoons milk, then slowly add the powdered sugar. If I's too thick, add a bit more milk until the desired consistency. Mix well to get out all the lumps.
Spread the frosting over the cake, spreading evenly to the edges.