Preheat oven to 350F (180C). Grease a sheet pan (also called half-sheet pan and measures 13x18 inches and about an inch deep).
Combine flour, sugar, salt, and baking soda in medium bowl. Set aside.
In a saucepan, bring peanut butter, water, and butter to a boil. Remove from heat and add the buttermilk and eggs. Pour over flour mixture and combine until smooth.
Pour the cake batter into the sheet pan and spread evenly. Bake at 350F (180C) for 20-25 minutes, or until toothpick comes out clean. Do not over bake. (Mine is typically done at 20 minutes.)
Prepare Peanut Butter Frosting
While cake is baking, add the powdered sugar to a medium bowl. Combine the peanut butter and butter in a saucepan and melt. Add buttermilk and bring to a boil. Remove from heat and add vanilla. Pour over powdered sugar and combine. Stir until no lumps remain.
When cake is finished baking, immediately spread peanut butter frosting over the cake. Be careful not to tear the cake while spreading it. Work quickly as the frosting will set up as it cools, making it harder to spread.