Preheat the oven to 350 degrees and grease a loaf pan with coconut oil or cooking spray.
In a food processor pulse oats until very fine. Grate carrots.
Combine flour, oats, pumpkin pie spice, cinnamon, nutmeg, salt and baking soda in a large bowl. Whisk together until combined.
In a medium bowl, whisk together pumpkin puree, applesauce, almond milk, egg, maple syrup, coconut oil, and vanilla extract. Add wet ingredients, mix together until combined. Fold in grated carrots until just combined.
Pour batter into loaf pan and sprinkle pumpkin seeds and chopped walnuts on top if desired.*
Bake for 45 minutes, or until a toothpick inserted into the middle comes out clean. Let cool completely and cut into pieces of your desired thickness. Store in the fridge for one week or freeze.