How to Make It
Preheat oven to 400°F. Butter a 2-quart soufflé dish.
Bring milk to a simmer in a pan over medium-high heat. Melt butter in a separate heavy pan over medium-high heat. Whisk in flour; cook for about 1 minute. (Do not let it brown.) Whisk in hot milk. Cook until thickened and smooth, about 1 minute. Reduce heat to low; whisk in yolks, one at a time, mixing well. Remove from heat and whisk in mustard, 1/2 cup cheese and spinach. Season with salt and pepper.
Using an electric mixer and a clean, dry bowl and beaters, beat whites until stiff peaks form. Stir 1/4 of whites into spinach mixture. Fold in remaining whites. Pour into soufflé dish.
Sprinkle remaining 1 Tbsp. Gruyère over top. Reduce oven temperature to 375°F; bake until lightly browned on top and firm around edges but still a bit jiggly in the middle, 30 to 35 minutes. Serve immediately, mixing firm edges with softer center in every serving.