Preheat your oven to 350°F.
Butter the inside of a 48-oz. soufflé dish. This is a dish that is that has straight sides and is oven safe.
Sprinkle the buttered dish with parmesan cheese. This keeps the soufflé from sticking and adds a teeny bit of flavor.
Cut the cheddar cheese into small cubes.
Separate the eggs. Put the egg whites in a bowl to mix separately.
Put egg yolks, milk, flour, mustard, salt, butter, and cheese in the blender. Blend on low to start and increase as needed to blend everything into a thick and smooth batter.
Pour the batter into a pan on your stove. Heat on low, stirring constantly, until the mix thickens. It will look about the same but will definitely have a change in consistency. This change happens quickly, so keep a close eye as you stir!
Once the mixture is somewhat thicker, turn of the heat and move pan off burner so it can cool slightly.
Use your hand mixer to beat the egg whites until they are white and stiff. This takes about five minutes on a medium high speed.
Pour the egg whites onto the cheese mixture.
Gently fold the egg whites into the cheese mixture, until it is a uniform color. Gently do this. The egg whites are what will make your cheese soufflé rise and you want to be very careful with them. Do not beat or over-stir this mixture. See notes for more about folding.
Pour the mixture into the prepared dish.
Bake for 25 minutes at 350 degrees until top is browned and springs back when lightly touched.