Add the butter to a light-colored saucepan over medium heat. Cook, stirring frequently, until the butter melts, foams, and develops golden-brown milk solids. Remove from the heat and allow the browned butter to cool slightly.
Place the Biscoff spread in a microwave-safe bowl and microwave for about 15-20 seconds until smooth when stirred together. Allow it to cool slightly.
In a large mixing bowl, whisk together the browned butter, melted Biscoff spread, brown sugar, and granulated sugar until smooth and well combined. Add the egg and vanilla extract and whisk until fully incorporated.
In a separate bowl, whisk together the flour, crushed Biscoff cookies, graham cracker crumbs, baking powder, baking soda, and salt.
Gradually add the dry ingredients to the wet ingredients, mixing just until no dry streaks remain.
Cover the dough with plastic wrap and refrigerate for 45–60 minutes. *see note*
Divide the chilled dough into 12 even portions, weighing them is the best move here for equal cookie sandwiches.
Place cookie dough balls on a parchment-lined baking sheet, leaving plenty of space between each cookie. Bake at 350°F (177°C) for approximately 14-16 minutes.
The cookies will spread while baking! Once removed from the oven, take a circular object (like a coffee cup or lid) and swirl around each cookie for a circle shape. Allow the cookies to cool on the baking sheet for about 10 minutes before transferring them to a wire rack. Cool completely.
In a medium sized bowl, beat the softened butter for 2-3 minutes with smooth. Add the powdered sugar, mixing on low speed until incorporated.
Add the marshmallow fluff, heavy cream, vanilla extract, and salt. Beat on medium speed until light and fluffy, scraping down the sides as needed.
Line a small baking sheet with parchment paper or wax paper. In a microwave safe bowl, melt the creamy biscoff spread for 15-20 seconds, stirring until smooth. Generously spoon about 1 tbsp of melted biscoff spread on the bottom of a cookie and place bottom side down, so the biscoff is directly touching the baking sheet. Repeat this for 6 cookies only! Place in freezer for 10-15 minutes or until melted biscoff spread is firm.
Once the cookies are completely cooled and the 6 cookies with melted biscoff spread are firm, pipe or spread a generous layer of marshmallow buttercream onto the flat side of one cookie (6 in total). Gently press two cookies together (one with biscoff spread, one with marshmallow buttercream) until you get a cookie sandwich. Serve immediately or refrigerate the assembled cookies until ready to enjoy.