Preheat the oven to 375°F and prepare an 8”x8” baking dish by greasing it with cooking spray, butter or coconut oil, or lining it with parchment paper.
In a large bowl, mix together the milk, Greek yogurt, eggs and vanilla extract. Set this aside while you prepare the dry ingredients.
In a medium-sized bowl, mix together the oats, brown sugar, baking powder, cinnamon and salt. Add this to the wet ingredients and stir until just combined. Fold in the grated carrots and chopped walnuts.
Pour the batter into the prepared baking dish and use a spatula to spread it out evenly.
Bake for 35-40 minutes or until an inserted toothpick comes out clean. Allow it to cool for 10 minutes before cutting into it and serving. Enjoy!