Preheat the oven to 350 degrees. Line a baking dish with parchment paper or lightly grease it and set aside.
In a medium bowl, whisk together the flour, baking soda, salt, ginger, cinnamon, and cloves. Set aside.
In a large mixing bowl, cream the butter and brown sugar together using an electric mixer until light and fluffy. Add the molasses, egg, and vanilla extract, mixing until fully combined.
Slowly add the dry ingredients to the wet ingredients and mix on low speed until just combined. Do not overmix.
Spread the dough evenly into the prepared baking dish. Bake for 18 to 22 minutes, or until the edges are set and the center is still slightly soft.
Remove from the oven and allow the cookie bars to cool completely before frosting.
Marshmallow Buttercream
With an electric mixer, beat the butter until smooth and creamy.
Add the marshmallow fluff and vanilla extract, mixing until fully incorporated.
Gradually add the powdered sugar, mixing on low speed. Add milk or cream a little at a time until the buttercream reaches a smooth and spreadable consistency.
Spread the marshmallow buttercream evenly over the cooled gingerbread cookie bars.