Preheat your oven to 350°F (175°C). Line a muffin tin with muffin liners or lightly grease it.
In a large mixing bowl, combine the whole wheat flour, rolled oats, baking soda, baking powder, salt, cinnamon, and nutmeg. Whisk together until fully combined.
In another bowl, mix together the honey (or maple syrup), pumpkin puree, applesauce, eggs, and vanilla extract. Stir until smooth and well blended.
Pour the wet ingredients into the dry ingredients, and gently fold them together using a rubber spatula until just combined. Be careful not to overmix.
If using, fold in the chopped nuts.
Divide the batter evenly among the muffin cups, filling each about ⅔ full.
Bake in the preheated oven for 20 minutes, or until the muffins are golden brown and a toothpick inserted into the center comes out clean.
Let the muffins cool in the pan for 5 minutes before transferring them to a wire rack to cool completely.