Follow your ice cream maker's instructions for pre-chilling the ice cream maker bowl. Some models require an overnight chill in the freezer, others can self-chill. If using the ice cream in a bag method, make sure you have enough ice and salt.
In a medium sized bowl or 2-cup measuring cup combine milk and half (about 2 oz) of the Cinnamon Toast Crunch cereal. Let sit at room temperature for 30 minutes.
Break the cinnamon stick in half and place it in a small pot over medium heat with the heavy cream. Bring the heavy cream to a low boil, then reduce the heat to low and simmer 20-30 minutes.
Place a wire mesh strainer over the mouth of a large bowl or measuring cup (at least 4-cup capacity). Pour the heavy cream through the strainer to remove the cinnamon stick pieces. Then pour the milk through the strainer to remove the cereal pieces. Discard the soggy cereal and cinnamon stick.
Add the rest of the Cinnamon Toast Crunch to the milk and heavy cream mixture. Set aside at room temp for 30 minutes.
In a large bowl vigorously beat two whole eggs with a whisk until pale and frothy, about 1-2 minutes. Set a timer so you know when to stop.Gradually whisk the sugar in to the eggs. Put a kitchen towel under your bowl to hold it in place if necessary. Once all the sugar is added, whisk vigorously 1 minute more. Place the wire strainer over the mouth of the bowl with the eggs. Strain the milk and heavy cream mixture into the bowl, removing and discarding the soggy cereal.Whisk to combine the eggs and cream. This is your ice cream base.
Transfer the ice cream base to an airtight container in the refrigerator and chill overnight (at least 8 hours).
The next day, pour your ice cream base into your ice cream maker and follow the instructions to churn it. If using the KitchenAid attachment, it should take about 20-30 minutes. The ice cream is done when it has climbed up to the top of the bowl and has a consistent texture all the way through. It will still be quite soft.
Transfer the churned ice cream to an airtight container. Press a sheet of plastic wrap across the surface of the ice cream to prevent freezer burn. Chill at least 2 hours before scooping.
Serve with crushed or whole pieces of Cinnamon Toast Crunch cereal on top.