Preheat oven to 350°F. Line a 13x9-inch baking dish with parchment paper or grease with butter or nonstick spray.
In a medium bowl, combine all-purpose flour, oats, baking soda, and salt. Mix until combined, then set aside.
To a large bowl with a hand mixer or stand mixer, add butter, granulated sugar, and brown sugar. Beat for 30 seconds or until light and fluffy.
To the butter, add the egg, peanut butter, milk, and vanilla. Beat until well combined.
Add the dry ingredients to the butter mixture. Beat until smooth.
Pour the mixture into the prepared baking dish and spread in an even layer.
Bake 30-35 minutes or until golden brown.
Immediately sprinkle chocolate chips on top of the base. Allow them to sit undisturbed for 1 minute or until softened, then spread evenly.
In a small bowl, combine powdered sugar and peanut butter. Gradually add enough milk to make it a drizzling consistency. Drizzle over the top. Allow the bars to set-up for 2 hours. Cut into squares and serve.