In a medium saucepan, combine the half-and-half and brown sugar. Cook over medium heat, stirring to dissolve sugar, about 4 minutes until bubbles form around the edges of the pan.
In a small bowl whisk together the egg yolks, pumpkin pie spice and salt. Gradually whisk about 1/2 cup of the hot half-and-half mixture into the egg mixture and continue to whisk until smooth. Pour the egg mixture into the half-and-half mixture in the pan. Cook and stir over medium heat until the mixture coats the back of a large metal spoon, about 4 minutes. Do not boil. Strain mixture through a fine mesh sieve into a large bowl. Stir in the cognac, if desired, and vanilla. Whisk the pumpkin into the mixture until thoroughly combined. Cover surface with plastic wrap to prevent a skin from forming and refrigerate until well chilled, at least 3 hours or overnight.
Pour the pumpkin custard into a 1- 1/2 or 2-quart ice cream maker; freeze according to the manufacturer's directions. Pack the ice cream into a freezer-safe container. Cover and freeze until firm, at least 3 hours or up to 3 days, before serving. Makes 10 (1/2-cup) servings.