Preheat the oven to 350°F (175°C). Grease a rimmed 10x15-inch baking sheet thoroughly.
Mix Dry Ingredients:
In a large mixing bowl, whisk together the flour, granulated sugar, and baking soda until well combined. Set aside.
Prepare Wet Ingredients:
In a separate bowl, beat the milk, eggs, and vanilla extract using an electric mixer set to low speed until smooth and incorporated.
Cook the Peanut Butter Mixture:
In a medium saucepan over medium heat, combine the water, unsalted butter, vegetable oil, and peanut butter. Stir continuously until the mixture is smooth and fully melted, approximately 5 minutes.
Combine and Bake:
Gradually stir the warm peanut butter mixture into the flour mixture until a cohesive batter forms. Pour the batter evenly into the prepared baking sheet, spreading it gently with a spatula.
Bake the Cake:
Bake in the preheated oven for approximately 20 minutes, or until a toothpick inserted into the center comes out clean. Remove from oven and allow the cake to remain warm while preparing the icing.
Prepare the Icing:
In a separate saucepan, melt the unsalted butter and peanut butter together over medium heat. Stir until smooth. Add the milk and vanilla extract, stirring until incorporated.
Finish the Icing:
Gradually whisk the confectioners' sugar into the peanut butter mixture until a smooth, spreadable icing forms, typically 3 to 5 minutes.
Frost the Cake:
Immediately pour the warm icing over the warm cake, using an offset spatula to spread it evenly. Allow the cake to cool completely before slicing and serving.
Notes
To prepare this Peanut Butter Sheet Cake gluten-free, substitute the all-purpose flour with a high-quality 1:1 gluten-free baking blend. Ensure the baking soda and confectioners' sugar are certified gluten-free as well.