Preheat oven to 375 degrees F if baking with a metal dish; 325 degrees F if using a glass dish.
Sift flour, sugar, baking powder, and salt together. Add graham cracker crumbs, peanut butter, shortening, milk, and vanilla. Beat mixture with electric mixer on low until moistened, and then beat on medium for 2 minutes. Add eggs and beat for 1 minute. Bake in greased 9-inch by 13-inch pan for 30 to 35 minutes. Do not remove from pan to cool.
For the frosting: mix all of the ingredients together. Pour into a saucepan and bring mixture to a boil. Boil for 1 minute. Cool slightly. With a wooden spoon handle, poke a few holes in the cake, and then pour the warm frosting over it.