Peel and finely grate the carrots. Chop the walnuts in a blender or mortar.
Mix the oats, chopped walnuts, flaxseeds, baking powder, cinnamon, and spices well.
Add the liquid ingredients: plant-based milk, agave syrup, and then the grated carrots. Stir everything together thoroughly until you have a smooth mixture.
Bake the baked oats for about 20-25 minutes at 180°C (350°F) in the oven.
Meanwhile, make the vegan cream cheese frosting. Combine the cream cheese with vanilla extract, agave syrup, and lemon juice.
Let the baked oatmeal cool slightly so it firms up, then spread the cream cheese topping on top.