In a medium bowl whisk egg yolks, brown sugar, pumpkin pie spice and pumpkin puree until well blended.
In a medium saucepan, heat heavy cream and milk until just boiling.
Whisk hot cream mixture, one ladleful at a time into egg and pumpkin mixture. Once about half of hot cream has been added, pour pumpkin mixture back into the sauce pan and return to heat.
Over a medium heat, whisk mixture frequently until thick and custard coats the back of a spoon, about 5 minutes.
Pour custard mixture through a fine sieve into a bowl placed over another bowl with ice. (Ice bath). Add bourbon, vanilla and kosher salt. Chill base several hours to overnight.
Freeze according to your manufacturers' instructions. Transfer to an ice cream container or freezer safe container and chill several hours to overnight.