Line a 9" x 9" baking pan with parchment paper, leaving some parchment hanging over two sides, so you can easily remove the brownies after baking.
Prepare a box of brownies as directed on the box (with appropriate ingredients).
Bake in the prepared 9" x 9" pan, according to the box directions, then allow to cool fully.
Once the brownies are cool, use the extra parchment to pull the brownies up from the pan, and move to a large cutting board.
Use a circle cookie cutter to cut circle brownie pieces the appropriate size to fit inside the bottom of your jars. I used 8oz. wide mouth jars and a 2 1/8 inch cookie cutter. Add brownie layer to jars.
Pull the ice cream and whipped topping from the freezer and allow to soften at room temperature for 10-20 minutes, just until the ice cream is soft enough to spread. Add a layer of ice cream on top of the brownie layer in each jar, then immediately move to freezer. If the whipped topping is now soft enough to spread, simply set in the fridge for the time being.
While the ice cream sets up, heat the heavy whipping cream in a bowl in the microwave just until hot, but not boiling. Remove from microwave, add chocolate chips and allow to sit for a minute. Stir to combine the chocolate and cream. Set aside and allow to cool to room temperature.
When the chocolate sauce has cooled to room temperature and the ice cream layer of the desserts has firmed up, spoon a layer of chocolate sauce on top of the ice cream. Move back to the freezer. I made 5 jars of dessert (filled as pictured) and had some sauce leftover. Reserve some sauce for topping the desserts just before serving.
Once the chocolate sauce has firmed up (about 10 minutes), add a layer of soft (but cool) whipped topping. Cover jars with lids, and move back to the freezer. Freeze desserts for at least 3 hours, or up to 5 days.
Cut up remaining bits of brownie that were left over after cutting out the circles. Store in an airtight container. When you are ready to serve the desserts, remove lids and add some brownie bites, a few chocolate covered espresso beans if desired, and a drizzle of the remaining chocolate sauce (warmed slightly).