Combine the cereal, cream, and milk in a large bowl. Cover and chill for at least 3 hours or overnight (the longer it sits the more cinnamon flavors will absorb into the ice cream base).
Pour the cereal mixture through a fine mesh sieve, and discard the cereal. Add the cream mixture and brown sugar to a large saucepan set over medium heat.
Cook the cream for 4 to 5 minutes, just until small bubbles begin to form around the edges of the pan.
Meanwhile, whisk the egg yolks and the granulated sugar in a separate bowl.
When the cream has begun to bubble just slightly around the edges, ladle about 1/2 cup of the cream mixture into the egg yolks, whisking constantly. Pour the egg yolk mixture back into the saucepan with the remaining cream.
Cook the cream and eggs, stirring constantly, until the mixture is thick enough to coat the back of a spoon, or until the temperature reaches 180°F.
Immediately strain the mixture through a fine mesh sieve into a separate large bowl set over a bowl of ice water, discarding any solids. Stir the custard constantly for 2 minutes. Stir in the vanilla, cinnamon, and salt. Cover and chill for at least 6 hours (but preferably overnight).
Pour the custard into an ice cream machine and churn according to the manufacturer's directions. For me, it usually takes around 20 minutes to get to soft-serve consistency, which is where we'll stir in the toffee.
Add the toffee bits during the last 5 minutes of churning.
Spoon the ice cream into a shallow airtight container. Pour the homemade caramel sauce over the ice cream and use a knife or a toothpick to swirl it into the ice cream.
Freeze the ice cream for at least 6 hours, but preferably overnight, before scooping and serving.