Preheat the oven to 350°F and line a medium baking dish (about 9x13 inches) with parchment paper.

Grate the zucchini on the coarse side of a grater, then squeeze firmly with clean hands or a clean towel to remove as much liquid as possible.

In a large bowl, combine the self-rising flour, salt, pepper, and chopped onion, and mix to coat the onion in flour.

Add the shredded cheddar cheese to the flour mixture and stir until the cheese is evenly coated and distributed.

Fold the drained zucchini into the flour and cheese mixture until it looks evenly combined.

In a separate bowl, whisk together the eggs, vegetable oil, and chopped parsley until smooth and slightly frothy.

Pour the egg mixture over the zucchini mixture and gently fold together until no dry flour remains and the batter is evenly combined.

Transfer the batter to the prepared baking dish and spread it into an even layer, smoothing the top.

Bake for 30 to 35 minutes, until the top is golden brown and the center feels set when lightly pressed.

Allow the zucchini slice to cool in the pan for about 10 minutes, then lift it out using the parchment.

Transfer to a wire rack if desired, let cool slightly, then slice into squares and serve warm or at room temperature.