Rinse the courgettes briefly in cold water, shake carefully and drain.
Peel the potatoes, chop roughly and boil in salted water for 25 minutes.
Finely chop the courgettes, add to a pan with a few tablespoons of water and a pinch of salt. Cook for 5 minutes until soft.
Drain the courgettes and blitz to a puree.
Drain the potatoes, cool, then squeeze through a potato ricer and mix with the courgette puree.
Finely chop the basil and marjoram. Peel the garlic.
Add the basil and marjoram to the vegetables and crush the garlic over. Add the Parmesan, egg and 2 tbsp olive oil.
Mix everything thoroughly and season with salt and pepper.
Remove the pistils from the centre of the courgette flowers.
Preheat the oven to 200°C (180°C fan, gas 6). Fill the courgette flowers with the vegetable puree, gently twist the tips and place them next to each other in a greased baking dish. Drizzle with the remaining oil and bake in the preheated oven for 15 minutes.