In a medium heavy-bottomed saucepan, cook the brown sugar and butter together over medium heat, stirring with a wooden spoon or carefully whisking. The sugar and butter will separate at first, but as the sugar melts it will become easier to blend them together. Cook and stir until the sugar melts and the butter/sugar mixture just starts to brown; it will start to smoke slightly as well.
Slowly add the cream, one cup at a time. The hot butter mixture will sputter and seize up as you add the cold cream, so continue to cook until the seized sugar dissolves again. Then add the salt and vanilla bean.
In a medium bowl, whisk together the egg yolks. Slowly add some of the hot butterscotch-cream to the yolks as you whisk and adding just enough to warm the yolks slightly. Pour the yolks back into the pot of hot butterscotch-cream and gently whisk to combine. Stir in the pumpkin puree and the pumpkin pie spice. Strain the mixture into another bowl.
Preheat the oven to 325°F.
Divide the custard into 8 to 12 small ramekins, espresso cups, or teacups. Place them in a roasting pan and fill the pan with hot water so that it comes halfway up the side of the ramekins.(Using cool water will prevent them from baking evenly.) Tent the pan with aluminum foil.
Bake until the custards are set, 25 to 40 minutes. This will depend on the temperature of the mixture when you put it in the oven and the size of your containers. It is best to check them after 25 minutes to gauge how much longer they need. Unlike a cake, you can open the oven and check them as often as you like without hurting them. To test if they are done, gently tap the side of each ramekin: If the custard ripples like water, it needs to bake longer. If it moves like set gelatin, then it is done. Be careful not to overbake them or they will be grainy and “eggy.”
Remove the pan from the oven and allow the custards to cool completely in the water bath, then remove them from the pan,cover with plastic wrap, and refrigerate for at least 1n hour and up to 3 days.
Before serving, sprinkle an even layer of the granulated sugar over each custard. Using a kitchen torch, lightly brown the sugar in a slow, even motion.