Trim and wash the spinach in several changes of cold water until no grit remains.
Put the spinach in a pan with only the water clinging to the leaves. Add 1 tbsp salt (15 ml), cover, and cook over medium heat until tender, about 5 minutes or less.
Drain the spinach. When cool enough to handle, squeeze gently to remove most moisture, then chop coarsely.
In a soup pot, sauté onion in butter over medium heat until the onion turns a pale gold. Add spinach and sauté uncovered 2 to 3 minutes, stirring to coat.
Add broth and milk. Grate in a very small amount of nutmeg, no more than 1/8 tsp (0.5 ml), and bring to a simmer, stirring now and then.
Stir in the grated cheese, taste and correct for salt, and turn off the heat.
Ladle into bowls and serve the crostini on the side.
