Put one cup of the cereal in a bowl and pour milk into it.
Let cereal sit in fridge for at least 6 hours (you can do less time, but for maximum flavor, I recommend 6).
Strain the milk from the cereal, reserving a cup of the milk. Put milk into a medium saucepan and heat with the salt and sugar over medium heat. Bring mixture to a simmer and then remove from heat.
Whisk egg yolks in a separate bowl.
Pour half of the hot milk mixture into the egg yolks, whisking constantly. Then pour that back into the saucepan with the rest of the milk. Cook mixture over low heat, stirring constantly, until it thickens enough to coat the back of the spoon.
Pour the cream into a separate large bowl place bowl in an ice bath.
Strain the warm milk mixture into the bowl of cream. Mix in vanilla and cinnamon and stir over the ice until cool.
Put the bowl into the fridge for at least 6 hours or overnight.
In the meantime, pre-heat oven to 350 degrees.
Put the remaining two cups of cereal in a bag and crush it a little bit.
Heat butter and brown sugar in a bowl in the microwave until it's melted. Whisk together until blended and pour it over the cereal in the bowl.
Spread the cereal over a parchment-lined cookie sheet in an even layer and bake at 350 degrees for about 10 minutes, until it's nice and caramelized.
Remove from oven, let cool, and break into small pieces.
When milk/cream solution is done chilling, process according to your ice cream maker manufacturer's instructions.
When the ice cream is almost done processing, mix in the Cinnamon Toast Crunch pieces. Then store the ice cream in a separate container and let freeze for another few hours, or overnight.
Serve ice cream in individual bowls and sprinkle a little bit more Cinnamon Toast Crunch on top if desired.