Preheat oven to 350°F. Grease and line a 9x9 inch baking pan with parchment paper, leaving an overhang for easy removal.

In a medium bowl, whisk together flour, baking soda, and salt. Set aside.

In a large bowl, cream together the butter, peanut butter, granulated sugar, and brown sugar until light and fluffy, about 2-3 minutes. Add eggs, one at a time, beating well after each addition. Stir in vanilla extract.

Gradually add the flour mixture to the wet ingredients, mixing until just combined.

Press the dough evenly into the prepared pan. Bake for 25-30 minutes, or until lightly browned and a toothpick inserted into the center comes out clean. Remove from oven and let cool slightly.

While the bars are cooling, prepare the peanut butter filling. In a medium bowl, beat together peanut butter and butter until smooth. Add powdered sugar, vanilla extract, and 2 tablespoons of heavy cream. Beat until smooth and creamy, adding an additional tablespoon of heavy cream if needed to achieve a spreadable consistency.

Using the back of a spoon or an offset spatula, spread the peanut butter filling over the warm bars in the pan.

Warm the Marshmallow Fluff in the microwave for a few seconds to make it easier to spread. Spread the Fluff over the peanut butter filling.

Allow the bars to cool completely in the pan before slicing into squares. Serve at room temperature.