In a small saucepan, melt butter over medium heat. Stir in flour until smooth and cook for 1 minute. Gradually whisk in milk, mustard, and salt. Bring to a boil, stirring constantly; cook and stir until thickened, about 1-2 minutes. Reduce heat to medium-low. Stir in all the shredded cheese until melted. Transfer to a large bowl.
Separate eggs. Place egg whites in a medium bowl; let stand at room temperature 30 minutes. In a small bowl, beat egg yolks until thick and lemon-colored, about 4 minutes. Stir in ⅓ cup hot cheese mixture, and then return all to remaining cheese mixture, stirring constantly. Cool completely for about 30 minutes.
Preheat oven to 325°F. Place eight ungreased 8 oz. ramekins in a baking pan.
With clean electric mixer, beat egg whites with cream of tartar on high speed until stiff but not dry, about 4-5 minutes. With a rubber spatula, gently fold egg whites into the cheese mixture.
Transfer mixture to prepared ramekins. Carefully, add 1 inch of hot water to baking pan. Pop into preheated oven and bake for 45 minutes or until tops are golden brown. Serve immediately.