Preheat & Prep: Preheat oven to 350°F (176°C). Grease a cake pan with oil or vegan butter and set it aside.
Wet Mixture: In a large bowl, whisk together peanut butter, non-dairy milk, vanilla, applesauce, vinegar, and espresso/coffee powder.
Dry Mixture: In another bowl, combine flour, sugar, cocoa powder, baking soda, baking powder, and salt.
Combine: Add wet ingredients to dry and mix until just combined.
Bake: Pour batter into prepared pan. Bake it for 30–35 minutes or until a toothpick inserted into the center comes out clean.
Cool: Let cake cool in pan for 10 minutes, then transfer to a rack to cool completely.
Frost: To make the frosting, beat peanut butter, salt, powdered sugar, and non-dairy milk until smooth (add milk gradually to control thickness). Then spread it evenly over the cooled cake.