In a small saucepan, bring the milk, thyme, onion, and cloves to a simmer. Turn off the heat and let steep for 15 minutes

Butter a 12-cup gratin dish or a 10-cup soufflé dish, which is traditionally deeper (a wider dish will rise less but will cook faster). Sprinkle the Parmesan along the inner sides of the dish.

Place the drained squash in a large bowl. Season to taste with salt and pepper, being aware that the Gruyère will also add saltiness. Set aside.

Preheat the oven to 400°F. 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, stirring often, until the mixture begins to turn golden brown.

Strain the milk, discarding the solids, whisk into the flour mixture, and cook, stirring constantly, until the mixture just begins to thicken, about 1 minute. Pour into the bowl of squash and mix well. Slowly add the egg yolks, two at a time, stirring constantly. Add the Gruyère and sage and mix well.

In the bowl of a stand mixer with a whisk attachment or by hand, whisk the egg whites with a pinch of salt until stiff peaks form. Gently fold into the squash mixture in thirds, making sure the whites are fully incorporated and no white streaks remain. Pour into the prepared dish.

Place the dish in the center of the oven, immediately lower the temperature to 375°F, 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.