Wash and cut the zucchini into coarse chunks. Rinse and gently pat dry the basil leaves with a tea towel;
Fill a stockpot with 1 quart (1dl) water, 1 quart (1dl) milk, a teaspoon of salt, and bring to a rolling boil. Then add the zucchini chunks, cover with a lid, and boil over medium heat for about 15 minutes. Be careful as the milk may boil, over, so leave the lid askew;
Turn the heat off, add the basil leaves, the butter, and the Parmigiano;
Blend into a smooth soup with an immersion blender;
Serve it very hot with a little toasted rustic bread.