In a saucepan off the heat, combine 1 1/2 cups (12 ounces/375 milliliters) cream, brown sugar, and molasses and stir to blend.
In a bowl, whisk together the egg yolks, cinnamon, nutmeg, ginger, and the remaining 1/2 cup (4 ounces/125 milliliters) of cream until well blended.
Place the saucepan over medium heat and cook, stirring frequently with a wooden spoon, just until bubbles form around the edges and the sugar dissolves, 4 to 5 minutes. Don't allow the mixture to come to a boil.
Immediately remove from the heat and, whisking constantly, slowly pour the hot milk mixture into the egg yolk mixture. When almost all of the hot liquid has been incorporated, slowly pour the warmed yolk mixture back into the saucepan, still whisking constantly. Place the saucepan over medium heat and cook, stirring constantly, until the custard [Editor's Note: Congratulations! You just made a custard!] is thick enough to coat the back of a spoon, 4 to 5 minutes.
Pour the hot custard through a strainer into a clean bowl, gently pressing the liquid through the sieve with the back of the spoon. Stir the pumpkin purée and vanilla into the custard just until blended.
Place the bowl with the custard into a larger bowl filled halfway with ice water and let cool for 30 to 45 minutes. Place a piece of plastic wrap directly onto the surface of the custard and refrigerate for at least 3 hours and up to 24 hours.
Prepare an ice cream maker with at least a 1 quart (1 liter) capacity according to the manufacturer’s directions. Pour the custard into the ice cream maker and churn until the custard reaches the consistency of thick whipped cream. Transfer to a plastic freezer container, cover tightly, and freeze until firm, at least 3 hours or up to 3 days.