Preheat Oven: Preheat your oven to 350°F (175°C). Grease and flour an 8-inch square baking pan or similar-sized dish.
Prepare Dry Ingredients: In a medium bowl, whisk together the flour, baking powder, and salt. Set aside.
Cream Butter and Sugar: In a large bowl, cream together the butter and sugar until light and fluffy.
Add Peanut Butter and Eggs: Beat in the peanut butter until well combined. Add the eggs one at a time, beating well after each addition.
Combine Ingredients: Gradually mix in the dry ingredients alternately with the milk. Begin and end with the flour mixture, mixing just until combined.
Add Vanilla: Stir in the vanilla extract.
Bake: Pour the batter into the prepared pan and smooth the top. Bake for 25-30 minutes, or until a toothpick inserted into the center comes out clean.
Prepare Topping: While the cake is baking, chop the chocolate bars or measure out the chocolate chips.
Cool and Top: Let the cake cool in the pan for about 10 minutes, then transfer to a wire rack to cool completely. Once cooled, sprinkle the chopped chocolate or chocolate chips over the top of the cake.
Serve: Cut into squares and enjoy!