Mix brown sugar and coffee liqueur into hot coffee and drop in cinnamon stick to steep. Let stand while making custard. Mix cocoa powder with cinnamon in a small bowl and set aside.
Whisk egg yolks, brandy and granulated sugar together in a large bowl set over a pot of boiling water until beginning to thicken. Whip with a whisk or an electric mixer until pale and at nearly tripled in volume, then remove from heat and mix in mascarpone cheese in batches until well incorporated.
Whip chilled heavy cream to stiff peaks then gently fold into mascarpone mixture.
Very quickly dip a biscoff cookie into coffee and let excess coffee drip away. Cookies can become mushy quickly so dip for less than a second in the coffee. Layer eight dipped cookies along the bottom of the medium baking dish, spread with a little less than 1⁄4 of the mascarpone mixture, then sprinkle with 1⁄2 a teaspoon of cocoa and cinnamon. Repeat with three more layers of eight cookies, following with mascarpone and cocoa in between each layer, pressing down very gently on each layer of cookies. Top final layer with remaining mascarpone and flatten by scraping with a spatula or knife. Save any remaining mascarpone mixture for serving with fruit or left over cookies. Cover loosely with plastic and chill in ridge for at least two hours.
Remove tiramisu from fridge and remove plastic. Using a sifter or fine strainer, dust top with remaining cocoa and cinnamon. Optionally create a design with bamboo skewers or kitchen twine on top of the tiramisu before dusting, then remove the skewers or twine to reveal the design.