Preheat oven to 350 degrees.

Combine cookie ingredients in large bowl and mix until completely incorporated.  NOTE:  Dough will be thick.

Using a medium sized cookie scoop {1.5 tablespoon}, scoop cookies onto a parchment lined cookie sheet.

Bake for 9-11 minutes, remove from oven and let cool on cookie sheet for 10 minutes before moving them to a cooling rack.  Repeat until all of the dough is baked.

Combine the butter, peanut butter and milk in a small saucepan over medium heat and bring to a boil.  Remove from heat, add powdered sugar and whisk until smooth. Stir in vanilla extract.

Pour {or spoon} frosting over cookies.  Use a knife or spoon to move excess frosting and be sure that the top of each cookie is completely covered.

Let frosting set and serve.  Keep your peanut butter Texas sheet cake cookies in an air tight container at room temperature for up to 3 days.