Although I didn't make it, here is my recipe (it back be halved and baked 9x13 pan)

Peanut Butter Sheet Cake

Cake:
1/4 cup creamy peanut butter
1 cup water
1/2 cup butter
1 cup sugar
1 cup brown sugar
2 cups flour
1 tsp salt
1 tsp baking soda
2 eggs
1/2 cup buttermilk
1 tsp vanilla

Frosting:
3/4 cup butter
6 tbsp buttermilk
1/2 cup peanut butter
3 1/2 cups powdered sugar
1 tbsp vanilla

1. Preheat oven to 375°F. Grease a 12x17 jelly roll pan (large cookie sheet with sides) lightly with non-stick cooking spray.  Set aside.

2. In a medium sauce pan add peanut butter, water, and butter and bring to a boil, stirring constantly. Remove from heat and let cool slightly. In a separate bowl, mix together sugar, brown sugar, flour, salt, and baking soda, until completely combined. Add to the peanut butter mixture with eggs, buttermilk, and vanilla.  Mix well.

3. Pour into your prepared pan and bake for 15-17 minutes or until toothpick inserted in the center comes out clean. Remove from oven and let cool 5 minutes.

4. To make the frosting, in a small sauce pan over medium heat, bring butter, buttermilk, and peanut butter to a boil, stirring constantly. Remove pan from heat and add powdered sugar and vanilla. Stir until completely incorporated and pour over slightly cooled cake. Let cool completely and serve. Enjoy!