In a medium saucepan vigorously whisk together all of the ingredients except for the vanilla.
Cook over medium heat, whisking constantly, until thickened, 10 minutes. (Once you can lift the whisk from the pudding and it leaves a faint shadow, it’s done.)
Strain the pudding through a fine-mesh sieve into a bowl, pressing pudding through sieve with a ladle (using a ladle here really helps separate the pumpkin solids from the silky pudding ). Whisk in vanilla.
Cool at room temperature for 10 minutes, press a layer of plastic wrap onto the surface of the pudding, and chill completely in refrigerator, 2 hours.