Put Cinnamon Toast Crunch 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 it into a medium saucepan and heat with the salt and sugar over medium heat. Bring mixture just to a simmer and then immediately remove from heat.
Whisk egg yolks in a separate heat-proof 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.
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 caramelized Cinnamon Toast Crunch pieces (save a little to top ice cream with if desired). Then store the ice cream in a separate container and let freeze for another few hours, or overnight.
Serve in individual bowls and sprinkle a little bit more caramelized Cinnamon Toast Crunch on top if desired.