1. To make the crust, butter a 9" springform pan. Break the chocolate wafers into a food processor fitted with a steel blade. Add the brown sugar and cocoa. Pulse until you have fine crumbs. Add the melted butter, pulsing to blend. Empty the pan and press the crumbs onto the sides with the back of a spoon, making an 11/2 "to 2" high border. Use a flat-bottomed glass to press the remaining crumbs firmly onto the bottom and into the crease of the pan.
2. Position the rack in the lower third of the oven and heat it to 325 degrees. Place the crumb-lined pan on a rimmed baking sheet and bake for 10-12 minutes. Remove from the oven and set aside to cool.
3. To make the filling, Place chocolate chips and water in a small microwave-safe bowl and melt on the defrost setting in 15-second intervals, stirring until smooth. Blend in the liqueur and ¼ teaspoons of the peppermint extract. Spoon the mixture over the crust, spreading evenly with the back of a spoon. Set aside.
4. Put the cream cheese in the bowl of a stand mixer fitted with the paddle attachment. Mix for 30 to 45 seconds at medium to low speed until smooth. Add the sugar in a steady stream, taking about 30 seconds, scraping the side of the bowl as needed. Mix JUST until very smooth. Blend in the eggs in 4 additions at 15-second intervals. Add the vanilla, remaining peppermint extract, and sour cream and mix for 30 seconds longer, scraping the side of the bowl again. DO NOT OVERBEAT.
5. Increase the oven to 350 degress. Pour the cheese filling over the chocolate, starting around the sides and filling in the middle—smooth surface with the back of a spoon. Be careful not to disturb the crumb crust. Bake for 50 minutes. TURN OFF THE OVEN, and without opening the oven door, please leave the cake in the oven for an extra hour. Remove the cake from the oven and set it on a rack to cool for 3 hours or longer. Refrigerate at least 24 hours before serving.
TO SERVE: Early in the day, before serving, run a thin knife around the edge of the pan and carefully remove the rim. Please transfer the cake to a flat platter with a damp napkin or several damp paper towels folded into a square placed under the metal bottom of the pan. This will keep the cake from sliding when it is sliced.
GARNISH AS FOLLOWS:
Display the Andes Candies around the cake starting at 12, 6, 9, and 3 o'clock, then fill in accordingly. Add fresh cranberries between the Andes Candies.
OR
DICE the Andes candies into ¼-inch pieces or coarsely chop peppermint candies and make a small mound in the center of the cake. Scatter the remaining candies over the top, graduating them outward from the mound.
Leave the cake at room temperature for about 1 hour before serving. Store it in the Refrigerator, covered with aluminum foil, for up to 1 week.