Healthy Breakfast Cake

Name: Healthy Breakfast Cake
Prep time: 10 min
Cook time: 45 min
Total time: 55 min
Cuisine: American
Ingredients: 2 cups rolled oats; 1 cup milk (of choice); 2 eggs; 1/4 cup maple syrup ((or honey)); 1 tbs olive oil; 1/2 tsp cinnamon; 3 tsp baking powder; 1/4 tsp salt; 2 cups coarsely grated carrot ((or raw butternut squash)); 1 Fuji apple (cored + coarsely grated); 1 cup powdered sugar; 2 tbs milk; 1 tsp vanilla extract