In a bowl, beat the yolks, brown sugar, and sugar with an electric mixer on medium speed until thick and dark beige, but still grainy, about 2 minutes; set aside.
Heat the milk and cream in a saucepan over medium heat until small bubbles frizzle along the pan’s inner rim.
Adjust heat so the mixture stays hot without coming to a boil.
Whisk about half of the hot milk mixture into the egg yolk mixture until smooth; then whisk this combine mixture back into the pan with the remaining hot milk mixture.
Whisk in the canned pumpkin; immediately decrease heat to very low—if you are working on an electric stove, move the pan to an unused burner just now set on low.
Cook slowly, stirring constantly, until the mixture thickens to the consistency of smooth cake batter and can coat the back of a wooden spoon, about 2 minutes.
Strain through a fine-mesh sieve into a clean bowl to remove any cooked egg; stir in vanilla and salt.
Refrigerate until cols for about 4 hours or overnight.
Just before you make the gelato, place the pumpkin custard and your ice cream machine’s dasher, if possible, into the freezer to shock them very cold, for no more than 10 minutes.
Freeze the custard in your ice cream machine according to the manufacturer’s directions.
Serve at once—or scoop into a container to store in freezer, tightly sealed, for up to 1 month; soften at room temperature for up to 10 minutes before serving.
*Pumpkin Chip Gelato—add 1/3 cup semisweet chocolate chips and 1/3 cup white chocolate chips to the machine when the gelato’s almost ready (or stir into the finished gelato as it is placed in a storage container.
*Spiced Pumpkin Gelato—add 1 teaspoon ground cinnamon, ½ t. ground ginger, and ¼ t. grated nutmeg with the vanilla; proceed as instructed.