Preheat the oven to 350°F. Lightly grease a muffin pan with cooking spray or line with muffin tins/liners. Set aside.
Mix together the dry ingredients by combining the flour, baking soda, salt, cinnamon, nutmeg, allspice, ginger, and pumpkin pie spice in a large mixing bowl. Stir the ingredients loosely together and set aside.
Mix together wet ingredients by combining the pumpkin puree, eggs, maple syrup, applesauce, almond milk, vanilla extract, and almond extract in a medium mixing bowl.
Make a small well in the dry ingredients and pour the wet ingredients into the dry ingredients. Fold the wet ingredients into the dry ingredients, loosely incorporating the ingredients. Be careful not to over-mix the batter (you should have a few light flour streaks). Fold in half of the walnuts and chocolate chips, if desired, and reserve the remainder for topping the muffins. This batter will be fairly thick.
Scoop the muffin batter into the prepared muffin tins, filling ¾ full to completely full for more voluminous muffin tops. Sprinkle each muffin with remaining walnuts and chocolate chips, if desired. Bake 18 to 20 minutes, or until a toothpick comes out from the muffin center cleanly or with a few crumbs. Cool the muffins in the muffin pan on a cooling rack for 5 to 10 minutes before serving, or allow to cool completely before storing.