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Preheat the oven to 400ºF. Butter a 12-cup gratin dish or a 10-cup soufflé dish. Sprinkle the Parmesan along the inner sides of the dish.
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Separate the eggs, reserving all of the whites and 6 of the yolks, separately.
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In a sauté pan over medium-low heat, gently cook the spinach until just soft, 2 to 3 minutes, adding a few tablespoons of water if the spinach is completely dry. When cool enough to handle, squeeze out the excess liquid, chop the spinach, and place in a large bowl. Season with a generous pinch of salt and pepper.
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In a small saucepan over low heat, melt the butter, making sure it doesn’t brown. Whisk in the rice flour and cook over medium-low heat for 3 minutes, stirring often. Whisk in the milk and cook, stirring constantly, until the mixture just begins to thicken, about 1 minute.
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Pour the mixture into the bowl with the spinach and mix well. Slowly add the 6 egg yolks one or two at a time, stirring constantly. Add the cheese, chives, and 1 teaspoon salt and mix well.
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In a separate large bowl or in a stand mixer fitted with the whisk attachment, whisk the egg whites with a pinch of salt until stiff peaks form. Fold them gently into the spinach mixture in thirds, making sure the whites are fully incorporated and no white streaks remain. Pour the mixture into the prepared dish.
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Place the dish in the center of the oven, immediately lower the temperature to 375ºF, and bake until the soufflé is golden brown on top and firm around the sides, about 30 minutes. If you want a more solid center or you’re using a deeper dish, bake for about 5 minutes longer. Try to keep the oven door closed to allow the soufflé to rise to its full potential. Serve immediately.