Preheat oven to 200 degrees C. Grease a 25cm heavy frypan and place it into the oven while it preheats.
Place the zucchini, milk, onion, eggs and vegetable oil into a blender and pulse 5 to 8 times until thoroughly mixed and the zucchini and onion have been chopped into very small pieces.
Mix together the polenta, plain flour, sugar, baking powder and salt in a large bowl. Pour the zucchini mixture into the cornmeal flour mixture, stirring to combine, and gently mix in the cheddar cheese.
Carefully pour the batter into the hot greased frypan, smooth it out with a spoon and cook until the cornbread is golden brown and a toothpick inserted into the center comes out clean, about 30 minutes.
You can also bake this in a greased baking dish, instead of the frypan.