Preheat oven to 400 degrees. Position rack in the center of the oven. Coat a 2-quart souffle dish or 6 individual (8-ounce) dishes with cooking spray. Coat with bread crumbs. Tap out excess; set aside.
Fill a bowl with ice and water; set aside. Place a steamer basket in a large saucepan; fill with 1 inch of water. Bring to a boil, and add the spinach. Cover, and steam until wilted, about 3 minutes. Drain, and plunge into ice bath to stop cooking. Let cool, and squeeze out excess water. Place the spinach in the bowl of a food processor; pulse until finely chopped; set aside. You should have about 1 cup.
Melt the butter in a small saucepan over medium heat. Whisk in flour, and cook, stirring constantly, for 3 minutes. Gradually whisk in the milk, and bring just to a simmer. Cook, stirring constantly, until slightly thickened, about 3 minutes. Stir in salt and pepper. Remove from heat, and set aside.
In a large bowl, whisk 2 egg yolks until blended. Whisk in a little white sauce to temper the eggs, then add the remaining sauce, whisking until combined. Add the cooked spinach and grated cheese.
Place the 4 egg whites and cream of tartar in the bowl of an electric mixer fitted with the whisk attachment. Beat on low until soft peaks begin to form. Increase speed to high; beat until stiff peaks form and egg whites are smooth.
Using a rubber spatula, transfer one- third of egg whites to spinach mixture; gently fold in until blended. Add spinach mixture to remaining egg whites; gently fold in until just combined. Pour into prepared dish or dishes.
Place souffle in oven, and reduce heat to 375 degrees. Bake until puffed and golden, 20 to 30 minutes. Serve.