Preheat the oven to 350 degrees. Line a 9x13 inch baking pan with parchment paper.
Cream the butter and peanut butter together until smooth. Add the brown sugar and granulated sugar and mix well. Add the eggs, one at a time, and the vanilla, beating until the batter is light and fluffy.
In a separate bowl, whisk together the flour, baking powder, and salt. Empty into the batter and mix on low until just combined. Stir in the peanut butter chips with a wooden spoon or rubber spatula.
Evenly spread the batter into the pan — it will be thick — and drizzle the chocolate syrup all over the top. Use the tip of a knife to swirl the chocolate through the batter.
Evenly sprinkle the chopped peanuts on top and add a dash of sea salt, if desired.
Bake for 35 to 40 minutes or until lightly browned. Cool in pan on wire rack before cutting.