Preheat your oven to 350°F / 175°C. Generously butter a 2-quart soufflé dish.
Trim, wash, and grate the zucchini.
Peel and finely chop the onion.
In a medium skillet, melt 2 tablespoons (30 ml / 1 fl oz) of the butter over medium heat and sauté the onions until just soft.
Add the grated zucchini and increase the heat, tossing and stirring frequently until the zucchini is tender and any excess water has evaporated.
Stir in the salt, basil, and a few grinds of black pepper.
Cook for another minute, then remove from the heat and set aside.
To make the béchamel base, melt the remaining 3 tablespoons (45 ml / 1.5 fl oz) of butter in a medium, heavy-bottomed saucepan over low heat.
Whisk in the flour to form a smooth paste (a roux) and cook for 2 minutes, stirring constantly. Gradually pour in the warm milk, whisking continuously to prevent lumps. Increase the heat to medium and continue whisking until the sauce is thick, smooth, and bubbly.
Remove the sauce from the heat.
Beat in the egg yolks one at a time, ensuring each is fully incorporated before adding the next.
Stir in the grated Parmesan cheese and the cooked zucchini mixture.
Taste and adjust seasoning with more salt and pepper if needed.
In a separate, large, clean bowl, beat the egg whites with a pinch of cream of tartar using an electric mixer until they form stiff, glossy peaks. Be careful not to overbeat.
Gently stir about a quarter of the beaten egg whites into the zucchini base to lighten it.
Then, carefully fold in the remaining egg whites in two batches using a large spatula, being careful not to deflate the mixture. The goal is to have a light, airy batter with minimal streaks of white.
Pour the mixture into your prepared soufflé dish.
Bake for 35 to 40 minutes, or until the soufflé is puffed, beautifully golden brown on top, and a skewer inserted into the center comes out mostly clean.
Serve immediately! Soufflés wait for no one.
Top with a drizzle of Hollandaise or cheese sauce, if desired.
Don't peek! Opening the oven door mid-bake can cause a sudden temperature drop, making your soufflé collapse. Watch its progress through the oven window.
Fold, don't stir.
When incorporating the whipped egg whites, use a gentle, sweeping motion with a spatula to maintain as much air in the batter as possible.