Pour the apple cider into a 4-quart or larger slow cooker. Whisk in the pumpkin puree until mostly smooth. A few small streaks of pumpkin are fine at this stage.

Add the sliced orange, cinnamon sticks, cloves, and lightly crushed allspice berries. Stir in the maple syrup and salt.

Cover and cook on LOW for 2 hours. The cider should become fragrant and fully warmed, with the pumpkin incorporated into the liquid. Avoid bringing it to a hard boil, which can make the cider taste overly cooked.

Carefully taste a small spoonful: If you want a sweeter cider, add a little additional maple syrup; if the flavor seems overly sweet, a few extra orange slices can help brighten it.

Stir in the vanilla extract during the final 5 minutes of cooking. This keeps its delicate flavor from becoming muted during the longer cooking time.

Place a fine-mesh strainer over a large heatproof bowl or pitcher. Carefully strain the cider to remove the orange slices and whole spices. Pressing gently on the solids is fine, but do not force the pumpkin through the strainer.

Return the strained cider to the slow cooker on the WARM setting for serving, or ladle it directly into mugs. Garnish with an orange slice or cinnamon stick if desired.