Turn the grill to its highest setting. Put the courgettes on an oven tray lined with baking paper, put on the top shelf of the oven closest to the grill, and cook for 45 minutes, carefully turning them once halfway through. The courgettes will look completely burned and blistered on the outside by the end, but that’s fine. Remove from the oven and leave to cool down slightly.
While the courgettes are cooking, put the oil in a small saucepan on the lowest heat. Add the strips of lemon zest, oregano, garlic and anchovy, if using, and cook gently for about 20 minutes, until the garlic has turned golden but not crisp. Turn off the heat and strain, keeping the oil and aromatics separate.
When the courgettes are cool enough to handle, cut a long slit through the skin of each one from top to bottom. Use a spoon to scrape out the flesh, then transfer to a colander placed over a bowl; discard the skins. Stir half a teaspoon of salt into the courgette pulp and leave for 15 minutes to drain.
To serve, spread the courgette over a serving plate and sprinkle the pine nuts on top. Drizzle with the lemon juice, then arrange the reserved garlic slices, lemon zest and a couple of oregano sprigs on top. Spoon over three tablespoons of the aromatic oil and finish with a sprinkle of dill.