Heat the milk, cream and miso in a small sauce pan over medium heat, whisking to dissolve the miso. Pour through a fine mesh strainer and add the vanilla.
In a heavy, but not dark sauce pan (so you can observe the caramel color), heat the sugar by itself over medium heat. Watch it closely until you see liquified sugar all around the outside of the pan. Once you see this, start to move the dry sugar around using a heat safe spatula.
Continue to gently move the sugar until it is all dissolved and browned to a copper penny color. You want it brown, but you don't want to burn your caramel unless you want the bitter taste. This can be tricking so just keep stirring and as soon as it is a dark golden brown, add the milk mixture. Be careful as it will bubble and sputter. Don't worry if some of the caramel initially hardens, it will melt again as it heats.
Continue stirring over medium heat until any hardened caramel melts but don't let the milk scorch or come to a boil. In a small bowl, whisk the cornstarch with a little of the hot milk then add back to the pot and whisk.
Cook, stirring the whole time, until it thickens. Strain through the fine mesh strainer into a bowl and cover directly on the surface with plastic wrap. Wrap up well, cool, and place into the fridge overnight.
The next day, churn in your ice cream maker according to the instructions. Mine takes about 10-15 minutes. Store in the freezer.