Put pumpkin in a medium saucepan and cook for about 5 minutes over medium heat to drive off moisture.
Add cream, milk, brown sugar, and salt and stir together.
Bring mixture just to a simmer at 170°, then remove from heat.
In a medium bowl, whisk egg yolks and brown sugar about 2 minutes.
Add in pumpkin pie spice, whisk to combine, then gradually whisk in 1 1/2 cups of the warm cream mixture to temper the eggs.
Drizzle and whisk the eggs from the bowl back into the saucepan, whisking constantly, then bring back to 170° over medium heat, also whisking constantly.
Add vanilla extract and brandy to ice cream and churn according to manufacturer's instructions. Transfer to an airtight container and freeze until solid, at least 4 hours.