Sift flour, baking powder, salt, allspice, and cinnamon together in a bowl. Set aside.
Beat the egg in a separate bowl, add the squash puree, maple syrup or molasses, milk, and butter.
Blend in the dry ingredients to form a smooth batter.
To make each pancake, spoon a heaping tablespoon of batter onto a lightly greased preheated griddle, flatten with a spoon to about ½ inch thickness, and cook until the bottom side is golden brown (3-4 minutes).
Turn and cook on the other side until golden brown (approx. 5 minutes longer).