Preheat your oven to 350°F (175°C) and grease a 9x13 inch baking pan.

In a large bowl, cream together softened butter, peanut butter, and sugar until smooth and fluffy.

Add eggs one at a time, blending well after each addition. Stir in the vanilla extract.

In a separate bowl, whisk together flour, baking powder, baking soda, and salt. Gradually mix into the creamed mixture, alternating with the milk for a smooth batter.

Pour the batter into the prepared pan and spread evenly.

Bake for 25-30 minutes or until a toothpick comes out clean from the center.

Let the cake cool in the pan for about 10 minutes, then transfer to a wire rack to cool completely.

For the frosting, beat softened butter and peanut butter together until creamy. Gradually mix in powdered sugar and adjust with milk to achieve desired texture.

Frost the cooled cake generously.