Combine gluten-free flour, baking powder, cinnamon, pumpkin pie spice, and salt in a large bowl.
Whisk eggs in a separate bowl. Whisk in almond milk, coconut oil, pumpkin puree, maple syrup, and vanilla extract. Fold in flour mixture until batter is just blended.
Preheat waffle iron according to manufacturer's instructions. Let batter rest, about 10 minutes.
Stir batter. Scoop 1/2 cup batter onto the preheated iron and spread to the edges. Close iron and cook until iron stops steaming, about 5 minutes. Repeat with remaining batter.
Substitute cow's milk for the almond milk if desired.
To keep waffles warm, place them in an oven preheated to 200 degrees F (95 degrees C).