Preheat the oven to 350 degrees.
In a medium bowl, combine the flour, crushed Biscoff cookies, baking soda, baking powder, and salt. Whisk together until combined. Set aside.
In a large bowl cream together the the butter and brown sugar until light and fluffy.
Add in the egg and vanilla extract and beat again until combined.
Add the cookie butter and mix until combined.
Add the flour mixture to the butter mixture and mix until everything is just combined.
Using a cookie scoop drop balls of dough onto the baking sheet. Bake for 10 minutes just until edges are set.
Remove from the oven and allow to cool on the baking sheet for 5 minutes before transferring to a wire cooling rack. Cool completely before frosting.
To make the frosting heat the cinnamon chips in the microwave in 30 second intervals, stirring after each heating, until melted. Let cool 5 minutes.
Place the melted cinnamon chips and butter in a bowl and beat with a mixer on medium high speed for 2-3 minutes or until smooth.
Add the milk and mix until well combined.
Stir in one cup of the powdered sugar along with the salt and mix on medium speed. Continue adding the powdered sugar until completely combined then turn the mixer to medium high and beat an additional minute.
Spread the frosting onto each cookei and sprinkle with crushed Biscoff cookies if desired.