Preheat your oven to 400°F. Grease an 8x8-inch pan (with high sides) or a similar 2-quart baking dish with butter. Evenly sprinkle 2 tablespoons of Parmesan onto the bottom and sides of the dish to coat the butter.
Melt 3 1/2 tablespoons of butter in a small saucepan over medium heat. Add the onion and cook until softened, about 3 minutes. Add all-purpose flour and cook, whisking constantly, until the floury taste is gone, about 1 minute.
Continuously whisk while adding the milk until the flour dissolves. Then, stir in kosher salt, black pepper, freshly grated nutmeg, garlic powder, and onion powder. Bring the mixture to a simmer, stirring constantly for 2 to 4 minutes.
Remove the saucepan from heat. Whisk in egg yolks one at a time, fully incorporating each before adding the next. Stir in the Gruyère, spinach, and 1 ounce Parmesan until well combined, ensuring that no large spinach clumps remain. Transfer the mixture to a large bowl.
Separately, add cream of tartar to egg whites. Beat on medium speed until firm, glossy peaks form, 3 to 4 minutes.
Transfer about 1/4 of the egg whites into the spinach mixture and stir until combined. Add the remaining egg whites and gently fold with a spatula until just combined with no large streaks. Transfer the mixture to the baking dish and smooth the top.
Place the baking dish in the oven and lower the temperature to 375ºF. Bake for 30-40 minutes or until the soufflé is puffed, golden brown, and free of wet egg streaks. Avoid opening the oven door before it’s done. Serve immediately; it will begin to deflate.