In a small mixing bowl, whisk together flour, brown sugar, baking powder, and baking soda.
In a medium-sized bowl, whisk together peanut butter, sour cream, and melted butter.
Stir flour mixture into peanut butter mixture until fully combined.
Stir in chocolate chips. The batter will have the consistency of cookie dough.
Grease a 6 quart slow cooker and evenly distribute batter on the bottom of the slow cooker bowl.
In a small bowl, whisk together sugar, cocoa powder, milk, and vanilla until smooth.
Pour chocolate sauce over the batter in the slow cooker.
Cook on high heat for 1 1/2 to two hours or until the sides of the pudding pull away from the slow cooker and appear solid. Keep in mind that the middle of the slow cooker takes longer to cook than the edges, so the middle will still be raw if the edges are at all undercooked.
Eat warm directly from the slow cooker plain or topped with chocolate syrup, whipped cream, or ice cream.