Step 1: Preheat your oven to 350°F (175°C). Lightly grease a 9x13 inch baking pan or line it with parchment paper, leaving an overhang on the sides for easy lifting.
Step 2: In a large bowl, cream together 1 cup of softened butter and 2 cups of granulated sugar until light and fluffy.
Step 3: Beat in 1 cup of peanut butter and 1 large egg, mixing until well combined.
Step 4: In a separate small bowl, whisk together 2 cups of all-purpose flour, 1 teaspoon of baking soda, and ½ teaspoon of salt.
Step 5: Gradually add the dry ingredients to the wet ingredients, mixing on low speed until just combined. Do not overmix.
Step 6: Press the cookie dough evenly into the prepared 9x13 inch baking pan.
Step 7: Bake for 20-25 minutes, or until the edges are lightly golden and a toothpick inserted into the center comes out with moist crumbs (the center may still look slightly underbaked).
Step 8: While the bars are cooling, prepare the frosting. In a medium bowl, combine the remaining ½ cup softened butter, ½ cup peanut butter, ½ cup milk, 1 teaspoon vanilla extract, and 4 cups powdered sugar. Beat with an electric mixer until smooth and creamy. If the frosting is too thick, add a tiny bit more milk, one teaspoon at a time.
Step 9: Once the cookie bars have cooled completely, spread the peanut butter frosting evenly over the top.
Step 10: Allow the frosting to set slightly before slicing into bars and serving. Enjoy!