Peanut butter sheet cake seemed to be very similar to a chocolate sheet cake recipe that I really liked. I ended up making half of the recipe below and it perfectly fit my 1/4 sheet pan. It is very peanut buttery and goes well with a glass of cold milk.
Peanut Butter Sheet Cake
Cake
2cups flour
2 cups sugar
1tsp. Salt
1 tsp baking soda
1cup peanut butter
1 cup butter
1cup water
1/2 cup buttermilk
2 eggs
Frosting
1/2 cup peanut butter
1/2 cup butter
6 Tbsp milk
1 tsp vanilla
4 cups icing sugar
Preheat oven to 350 F. Grease a half sheet pan, 13”x18”. Combine flour, sugar, salt and baking soda in a medium bowl and set aside. In a 2 quart sauce pan on medium heat, bring peanut butter, butter and water to a boil and set aside off of the heat. Add buttermilk and beaten eggs to the peanut butter mixture and stir in. Add in dry ingredients and mix to a smooth batter. Pour into prepared pan and level off the batter. Bake 20-25 minutes or until toothpick inserted in center comes out clean. (If you make a half recipe check cake at 15 minutes)
When cake is removed from oven immediately make the frosting. Heat the peanut butter and butter in a saucepan to melt. Add milk and bring to a boil. Remove from heat and add vanilla and icing sugar beating until smooth. Pour the frosting onto the still warm cake and quickly spread frosting before it begins to set up.