In a large bowl, combine the flour, salt, sugar and yeast. Gradually add the warm water and olive oil, kneading until a smooth, elastic dough forms (about 10 minutes by hand or 5–6 minutes using a mixer with a dough hook).
The dough should be soft and no longer stick to your hands. Shape it into a ball, place it in the bowl, cover with a clean cloth and leave to rise in a warm place for 1–1.5 hours, until doubled in size.
Mix the marinara sauce with the pesto and heat briefly over medium-high heat to reduce slightly.
In a pan, sauté the courgette and onion in a tablespoon of olive oil. Add the spinach and garlic and cook for another 1–2 minutes until the spinach has wilted. Season with salt and pepper.
In a bowl, combine the mozzarella, spinach mixture, courgette, onion, sun-dried tomatoes and herbs.
Divide the risen dough into 8 equal pieces and shape them into balls. Stretch or gently roll each ball into a circle about 15 cm in diameter.
Spread about a teaspoon of sauce over one half of each circle and add a generous spoonful of the prepared filling. Fold the dough over to create a half-moon shape and seal the edges like a dumpling. Brush the tops with olive oil.
Replace the grill grates with a pizza stone. Light the burners: set the centre burners to medium and the outer burners to maximum. Preheat the grill with the stone to 300–350°C.
Once the grill reaches the desired temperature, reduce the burners under the stone to low and the outer burners to medium.
Transfer the mini calzones onto the hot stone (a pizza peel or a board dusted with flour or semolina works best). Close the lid and bake for 6–8 minutes, until golden, crispy and well cooked on the bottom.
Once baked, you can sprinkle them with grated Parmesan. Let them rest for 1–2 minutes, then serve with your favourite dip.