Pour 750ml boiling water into a medium pan and add a pinch of salt. Bring to the boil. Slowly whisk in your polenta. Turn the heat right down. Cover. Simmer for 25 mins, stirring a few times till the polenta is thick, soft and comes away from the sides of the pan.
While the polenta cooks, finely dice your courgettes into chunks around 1 cm across. Warm a deep frying pan over a high heat for 1 min. Add the courgettes in a single layer (you may need to do this in batches) and season with salt and pepper. Fry for 5-7 mins, turning once, till a little charred all over. Season as you cook. Don’t add oil – the idea is to draw out all the moisture and get a slightly smoky taste.
Tip the courgettes into a bowl when they’re charred. Finely chop the chervil, leaves and stalks, and the chives. Add them to the courgettes, holding a pinch back for garnish. Wipe the frying pan clean and fill with water. Cover and bring to the boil.
Peel and grate the garlic and add to the polenta after it has cooked for 20 mins. Stir. Finely grate most of the Parmesan into the simmering polenta, which should be nearly cooked. Finely grate the lemon zest. Stir it into the polenta and squeeze in the juice. Stir and take off the heat.
Stir in the courgettes and herbs. Taste and add a little more salt and pepper if it needs it. Cover and leave to sit while you cook the eggs.
When the pan water is boiling, crack 1 egg into a cup and slide into the pan. Repeat with the other eggs (you need a wide pan to cook all 4 at once). Simmer for 2-3 mins till the yolk is set to your liking.
Spoon the polenta into bowls. Top with 2 eggs each. Grind over some pepper. Sprinkle over the remaining herbs and Parmesan.