Preheat oven to 350 degrees F. Line a 8-inch-by-8-inch square baking pan with parchment paper so that it overlaps on all sides.
In a mixer fitted with a paddle attachment (or in a large bowl using a handheld mixer), beat butter, peanut butter, granulated sugar, and brown sugar until light and fluffy, about 1 minute. Scrape down the sides of the bowl and add the egg and vanilla extract; beat until combined.
Add the dry ingredients to the bowl and beat until just combined, scraping down the sides of the bowl as needed.
Add 2/3 of the batter to the bottom of the prepared baking pan. Press the dough evenly into the bottom of the pan. Add the chocolate bars in an even layer, breaking them apart as needed, to the top of the batter. Press down slightly on the bars so they adhere to the batter. Spread the marshmallow fluff evenly over the chocolate layer. Sprinkle the remaining 1/3 of the batter evenly over the marshmallow cream.
Bake for 25-30 minutes, or until golden brown. Allow to cool completely before cutting into squares.