Pour 2 cups of whole milk into a medium heavy bottom saucepan. Whisk in the brown sugar and heat over medium until an instant-read thermometer reads between 180 and 190 degrees. Continue to heat and cook at this temperature for 5 minutes, stirring constantly.
Remove the milk and brown sugar mixture from the heat and allow it to cool 5 minutes. In a medium non-reactive bowl whisk together the egg yolks, salt and 1/4 cup granulated sugar until foamy and slightly thickened. Slowly temper the eggs by drizzling spoonfuls of the hot milk mixture into the eggs while whisking constantly. Once about half the milk is whisked into the eggs, pour the egg and milk mixture into the remaining hot milk mixture and stir until well blended. Return the pan to the stove and heat on medium. Stir constantly with a wooden spoon until the mixture reaches 185 degrees on an instant-read thermometer or is thick enough to cot the back of the spoon. Make sure the mixture does not boil.
Add the canned pumpkin, cinnamon, ginger, nutmeg and allspice to the hot milk/egg mixture. Carefully emulsify the mixture with a stick or hand blender or regular blender.
Pour the 1 cup of heavy cream in a clean large stainless-steel or glass bowl set over an ice bath. Pour the pumpkin mixture into the cream and add the vanilla and bourbon. Whisk until fully incorporated. Stir occasionally, about every 5 minutes or so, until the mixture has fully cooled. Remove the mixture from the ice bath and dry off the bottom of the bowl if necessary.
Cover the Gelato with plastic wrap and chill in the refrigerator overnight or at least 8 hours. When ready prepare the Gelato using your ice cream maker and follow manufacturer instructions. Store the frozen Gelato in an airtight container until ready to serve.
If you prefer a harder frozen Gelato, omit the bourbon.