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 cup water, 1 cup 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.