Preheat the oven to 375°F. Butter an 8-cup soufflé dish and sprinkle the bottom and sides with 2 tablespoons of the shredded cheese.

In a medium saucepan, heat the milk until scalded; add the cornstarch mixture and stir over medium heat until thickened. Stir in the salt and nutmeg and set aside.

In a large skillet, melt the butter over medium heat and cook the onion until softened, about 5 minutes. Add the spinach and cook just until heated through and still slightly crisp, about 1 minute; drain off any liquid. In a blender or food processor, purée the spinach and egg yolks until the spinach is minced. Stir the spinach mixture into the cornstarch-thickened sauce. Mix in the remaining cheese.

In a large bowl, beat the egg whites until foamy. Add the cream of tartar and beat until stiff, glossy peaks form. Fold one-fourth of the beaten egg whites into the spinach mixture. Fold this mixture into the remaining egg whites. Spoon the batter into the prepared soufflé dish; smooth the surface. Bake in the oven for 35 minutes, or until puffed and golden brown.