Set the caramelized white chocolate in a medium sized heatproof bowl.
In a small bowl mix together 2 tablespoons milk and the cornstarch. Set aside.
Warm the 1 cup milk, sugar, heavy cream and salt together in a pot and whisk until the sugar has dissolved. Pour in the cornstarch mix and whisk.
Once the liquid has start to thicken slightly on the bottom, stir and remove from heat. Pour over the chocolate and stir until the chocolate has melted.
Add the salt and vanilla and stir to combine. Let cool to room temperature, then cover with plastic wrap and chill in the fridge until cold.
It may develop a thin film on top (as a pudding would) so whisk it right before pouring into molds and freezing.
Freeze, adding the sticks when the mixture is firm enough to hold the stick in place.