Preheat oven to 350°F, and coat a 9” round pan with nonstick cooking spray.
In a medium bowl, whisk together oats, flour, baking powder, baking soda, cinnamon, nutmeg and salt.
In a separate bowl, whisk together oil, eggs and vanilla. Add Greek yogurt, and stir until no large lumps of yogurt remain. Stir in the maple syrup.
Slowly add 1/3 of the dry mixture and half of the milk, stirring gently until just combined. Keep alternating between the dry mixture and milk until all ingredients are added. (For best results, add the oat mixture in 3 equal parts and the milk in 2 equal parts.) Gently fold in the carrots and zucchini.
Spread batter into the prepared pan.
Bake for 35-40 minutes or until the center feels firm to the touch and a fork inserted into the center comes out clean.
Cool completely in the pan before slicing and serving.