Preheat the oven to 350 degrees F. Grease a 9-by-13-by-2-inch baking dish with butter.
Using an electric mixer, cream the butter, granulated sugar, brown sugar and 1/2 cup of the peanut butter. Add the egg and vanilla. Sift the flour with the baking soda and the salt. Mix the oatmeal into the flour and stir the flour into the creamed mixture. Spread the batter in the baking pan. Sprinkle the butterscotch chips over the batter and bake for 20 to 25 minutes, until browned around the edges.
Whisk together the confectioners' sugar, milk and the remaining 1/4 cup of the peanut butter until smooth, then spread the glaze evenly over the warm bars. Allow to cool completely before cutting into squares.
Adaped from "Home Cooking with Trisha Yearwood" by Trisha Yearwood (c) Clarkson Potter 2010. Provided courtesy of Trisha Yearwood. All rights reserved.