Place the grated courgette, flour and grated Parmesan in a bowl and mix together well.
Squeeze into walnut-sized balls and then gently flatten.
Heat the oil in a deep frying pan and, working in batches if necessary, fry the fritters for 2–3 minutes on each side, until golden.
Meanwhile, bring a large saucepan of water to a gentle simmer and stir with a large spoon to create a swirl. Carefully break 2 eggs into the water and cook for 3 minutes. Remove with a slotted spoon and keep warm. Repeat with the remaining eggs.
Serve the fritters topped with the poached eggs and sprinkled with pepper.