Preheat your oven to 350°F (175°C) and line a 9"x13" baking pan with parchment paper.

In a large mixing bowl, combine peanut butter and melted butter until smooth. Add white sugar and brown sugar, blending thoroughly.

Incorporate the eggs and vanilla extract, whisking until combined and smooth.

In a separate bowl, sift flour, baking powder, and salt. Set aside.

Fold the dry ingredients into the wet mixture until no white streaks remain, maintaining a thick batter.

Pour the batter into the prepared baking pan, spreading it evenly.

Bake for 25-30 minutes, starting to check at 25 minutes. Edges should be set and center slightly wet.

Remove from the oven and cool in the pan for at least 30 minutes before slicing.