Preheat oven to 350°F (175°C). Grease an 8x8-inch baking dish with coconut oil or cooking spray.
Add 1 cup of rolled oats to a blender and process into a fine flour. Set aside the remaining 1 cup of whole oats.
In a large bowl, whisk together the whole oats, oat flour, baking powder, protein powder, salt, cinnamon, ginger, and nutmeg.
In a separate bowl, whisk together almond milk, eggs, melted coconut oil, maple syrup, and vanilla extract until smooth.
Pour the wet ingredients into the dry ingredients and stir to combine. Fold in shredded carrots, raisins, and walnuts.
Transfer the batter to the prepared baking dish. Spread into an even layer and bake for 30 to 35 minutes, until the top is golden and set.
Allow to cool for at least 10 minutes.
Stir together Greek yogurt, cream cheese, maple syrup, and vanilla extract until smooth.
Spread the icing over the cooled oatmeal bake. Slice into 6 portions and serve immediately, or refrigerate for meal prep.