Butter a 1½ quart soufflé dish and dust it with ¼ cup grated Parmesan cheese.
In a large, heavy saucepot, melt the butter. Stir in the chopped onion and cook until soft. Stir in the minced garlic and cook until fragrant. Add the flour to make a roux, and stir and cook for about 3 minutes.
Add the milk, whisking, and simmering the mixture. Continue to whisk and cook until smooth and thick. Remove the pan from heat.
Whisk in the Gruyere cheese. Whisk in the egg yolks. Whisk in the squash puree.
Beat the egg whites with a pinch of salt until they form soft peaks. Whisk about ¼ of the egg whites into the squash mixture to lighten it.
Fold the remaining egg whites into the squash mixture. Spoon the mixture into the prepared soufflé dish and sprinkle the top with the remaining grated Parmesan cheese.
Bake in the center of a preheated 375-degree oven for about 45 to 50 minutes. The top will be golden and puffed. Remove the soufflé from the oven and serve immediately.
Nutritional analysis (varies, estimate per one cup serving): 230 calories, 11 grams protein, 8 grams carbohydrates, 18 grams fat, 770 mg. sodium, 2 grams fiber.