Peel the carrots and zucchini and grate them on the largest side of a cheese grater. Dice the onion and place all the veggies into a large bowl.
Add flour and baking powder to the bowl and stir to combine.
Add whisked eggs, oil, and cheese to the bowl and stir again to combine. Season mixture with salt, keeping in mind that the cheese will add a burst of salty/savory flavor.
Brush a 9 in. or 11 in. pan with oil. Pour the batter into the pan and bake at 350°F for 60 minutes.
Let the cake cool for a few minutes in the pan. Slice and enjoy!