Preheat the oven to 350ºF and grease an 8-inch square baking dish. Press a piece of parchment paper into the bottom of the dish to ensure easy removal later. (This is optional, but makes clean-up easier, too.)
In a large bowl, combine the eggs, coconut milk, and vanilla extract. Whisk well to combine.
Add the rolled oats, coconut sugar, baking powder, cinnamon, ginger, nutmeg, and salt. Stir well, then fold in the shredded carrots, walnuts, and raisins.
Pour the mixture into the prepared pan and spread it out evenly. Sprinkle a few extra walnuts on top, if you like. Bake at 350ºF for 40 to 45 minutes, or until the top feels dry to a light touch. Let it cool in the pan for 15 minutes before slicing.
Slice into 6 large pieces (my preference for meal prep) or slice into 9 squares if serving it as part of a brunch spread. Leftovers should be stored in an airtight container in the fridge for up to 5 days. Reheat individual slices in the air fryer for 8-10 minutes as it preheats to 350ºF. (Or microwave for 20-30 seconds.)
Notes
Nutrition information is for 1 of 6 large slices. This information is automatically calculated and is just an estimate, not a guarantee.Sweetener Note: As written, this baked oatmeal tastes like a light-sweet carrot cake without the need for extra maple syrup or frosting. You can reduce the sugar to a 1/2 cup if you prefer a less-sweet brunch option. I don't recommend swapping the granulated sugar for maple syrup, as the results will be more gummy, but feel free to experiment with it.