Preheat the oven: Set your oven to 180°C (350°F) to preheat.
Prepare the vegetables: Grate the zucchini and carrot. Place the grated zucchini in a clean kitchen towel and squeeze out the excess moisture. Finely chop the onion and red pepper, and set them aside.
Cook the vegetables: In a large pan, heat the olive oil over medium heat. Add the onion and cook for 3-4 minutes, until softened. Then, add the grated carrot and diced red pepper. Cook for another 3 minutes, stirring occasionally.
Mix the batter: In a large mixing bowl, combine the grated zucchini, cooked vegetables, fresh parsley, eggs, milk, flour, salt, and black pepper. Stir well to combine.
Add cheese: Fold in the grated mozzarella cheese into the mixture.
Bake: Pour the vegetable mixture into a greased baking dish and spread evenly. Bake in the preheated oven for 30-35 minutes, or until golden brown on top and cooked through.
Serve: Allow the bake to cool for a few minutes before slicing. Serve warm and enjoy!