Preheat the oven to 375°F (190°C). Grease a 2-quart soufflé dish with butter and lightly dust it with flour.

In a large skillet, wilt the spinach over medium heat until it is completely wilted. Remove from heat and let it cool.

Squeeze out the excess moisture from the spinach and roughly chop it.

In a large mixing bowl, whisk the egg yolks until pale and creamy. Add the grated Parmesan cheese, milk, flour, salt, and nutmeg. Mix well.

In a separate mixing bowl, beat the egg whites until stiff peaks form.

Gently fold the beaten egg whites into the yolk mixture, followed by the chopped spinach and shredded Gruyere cheese.

Pour the mixture into the prepared soufflé dish and smooth the top with a spatula.

Bake in the preheated oven for about 35-40 minutes, or until the soufflé has risen and turned golden brown on top.

Remove from the oven and serve immediately while the soufflé is still puffed and airy.