Preheat oven to 350 degrees F. Butter the bottom and sides of a 8 inch metal baking pan. Put a long piece of parchment paper in the bottom of the pan, letting the parchment extend up two sides of the pan and overhang slightly on both ends. (This will make it easy to remove the bars from the pan after they have baked.) Butter the parchment.
In a small saucepan over medium heat, melt butter. Whisk in sugar and bring to a boil, whisking frequently; boil 1 minute. Set aside to cool for 5 minutes.
In the bowl of a stand mixer fitted with the paddle attachment, beat together cream cheese, confectioners’ sugar, vanilla extract and peppermint extract until combined, about 1 minute.
In a medium bowl, sift together flour, cocoa powder and salt; whisk until combined.
In a large bowl, whisk together eggs until combined. Whisk in melted butter-sugar mixture until well combined. Stir in flour mixture until just combined, followed by Thin Mint Cookies.
Spread half of brownie batter into the prepared baking dish, followed by cream cheese layer. Distribute the remaining brownie mixture in 8 dollops over the cheesecake layer and spread evenly. Swirl in with a knife or spatula.
Bake for 24-28 minutes, until brownies and cheesecake are set. A knife inserted into the cheesecake mixture should come out clean and the edges will be lightly browned.
Let cool completely in pan on a cooling rack before lifting out the parchment paper to remove the brownies.