In a saucepan, whisk together the milk, 1 cup cream, brown sugar, egg yolks and salt.
Over medium heat, cook the custard while whisking constantly, just until it's steaming hot. Don't let it come to a boil.
Remove from the heat, and pour through a mesh strainer to remove any bits of cooked egg.
Whisk the vanilla and the banana puree into the ice cream base.
Cover and refrigerate until well chilled, or overnight.
When you're ready to churn the ice cream, use an electric mixer to whip the remaining 1 cup cream until soft peaks form, then whisk the whipped cream into the chilled ice cream base.
Churn the ice cream in your ice cream maker, according to the manufacturer's instructions, until it's a thick, soft-serve consistency.
Transfer the churned ice cream to a lidded container. Drizzle with the caramel sauce or toffee sauce and sprinkle with toffee bits, then use a spoon to swirl everything together, leaving visible streaks of caramel.
Freeze the ice cream for 6-8 hours, or until firm enough to scoop.
Serve the ice cream with more of the caramel/toffee sauce and toffee bits.