Preheat the oven to 375 degrees and grease a muffin pan.
In a small bowl, whisk together the flour, baking powder, cinnamon, and salt. Set aside.
Grate the carrots and mash the banana. I use a food processor, but you can also grate the carrots with a hand grater and mash the bananas with a fork.
In a large bowl, stir together the eggs, mashed banana, coconut oil, maple syrup, water, and vanilla extract. Add the dry ingredients, and stir just to combine. Then stir in the carrots, raisins, and walnuts.
Transfer the batter to the muffin pan. Bake for 20 to 22 minutes, or until a toothpick inserted in the center of a muffin comes out clean.
Leave the pan on a cooling rack for 5 minutes before removing the muffins from the pan to cool completely. Store in an airtight container at room temperature for up to 3 days, or freeze for later.