Preheat oven to 350°F and grease a 9-inch round cake pan.
In a large bowl, mix together the peanut butter, brown sugar, egg, vanilla extract, and buttermilk until well combined.
Add the flour, salt, and baking soda to the peanut butter mixture. (The batter will be dry, but the undrained zucchini will bring in moisture.)
Fold in the shredded, undrained zucchini.
Pour the batter into the prepared cake pan and bake for 25-30 minutes, or until an inserted toothpick comes out with a few crumbs, but no wet batter.
Let the cake cool before adding the melted peanut butter and chopped peanuts (optional).