Let egg whites stand at room temperature 30 minutes. Grease a 1-1/2-qt. souffle dish; dust lightly with flour.
Preheat oven to 350°. Microwave broccoli and water, covered, on high until broccoli is tender, 2-3 minutes. Let stand for 5 minutes; drain. Pulse broccoli in a food processor until blended.
In a small saucepan, melt butter over medium heat. Stir in flour and cayenne pepper until smooth. Gradually whisk in milk. Bring to a boil, stirring constantly; cook and stir until thickened, 1-2 minutes. Transfer to a large bowl; stir in cheese, mustard, salt, pepper and broccoli. Whisk a small amount of hot mixture into egg yolk; return all to bowl, whisking constantly. Cool slightly.
In another bowl, beat egg whites with cream of tartar until stiff but not dry. With a rubber spatula, gently stir a fourth of the egg whites into broccoli mixture until no white streaks remain. Fold in remaining egg whites. Transfer to prepared dish. Bake until top is puffed and center appears set, 30-35 minutes. Serve immediately.