Preheat the oven to 350°F (175°C) and line a 12-cup muffin tin with non-stick silicone liners or parchment paper.
In a large mixing bowl, whisk together the whole wheat flour, baking soda, baking powder, salt, and pumpkin pie spice until evenly distributed.
In a separate medium bowl, whisk the pumpkin purée, unsweetened applesauce, maple syrup, eggs, and vanilla extract until the mixture is homogenous.
Pour the wet ingredients into the dry ingredients bowl and fold gently using a spatula until just combined; do not overmix to avoid a tough texture.
Distribute the batter evenly across the 12 muffin cups, filling each approximately three-quarters full.
Bake for 18 to 22 minutes, or until a toothpick inserted into the center of a muffin comes out clean or with dry crumbs.
Remove the tin from the oven and allow the muffins to rest for 5 minutes before transferring them to a wire rack to cool completely.