Preheat the oven to 350F degrees and place the oven rack in the middle of the oven.
Line a 9x13 inch pan* with parchment paper, leaving an overhang around the edges. Or line with aluminum foil and lightly grease.
In a medium bowl whisk together the flour, baking powder and salt.
In a separate large bowl beat together the butter, brown sugar and white sugar until soft.
Beat in the peanut butter. Then mix in the egg and egg yolk until smooth.
With the mixer on low speed, mix the flour mixture into the peanut butter mixture about ½ at a time.
Remove about 1 cup of batter from the bowl.
Press the rest of the peanut butter dough into the bottom of the lined pan, to form an even layer.
Bake the peanut butter layer in the preheated oven for 25 minutes, or until the top looks fully set.
Remove the pan from the oven (keep the oven turned on). Carefully spread the entire jar of marshmallow fluff on top of the peanut butter layer.
Pinch of pieces of the reserved peanut butter cookie dough, flatten them slightly into pieces about 1 inch in size and place on top of the marshmallow layer. You do not need to entirely cover the marshmallow layer - mine was about 80-90% covered.
Place the pan back in the oven and bake for 10 minutes, or until the peanut butter layer on top is set.
Remove the pan from the oven and let the bars cool at room temperature for at least 1 hour before slicing.
Before slicing, lift the bars out of the pan using the overhang of the parchment paper/aluminum foil and place on a cutting board.
Slightly grease a thin, sharp knife with non-stick cooking spray (this is optional - but helps to avoid the marshmallow layer sticking onto the knife) and slice the bars.