In a large pot over medium high heat, add butter, onion, carrot and celery. Cook for about 5 minutes, stirring frequently.
Add the flour and stirring constantly, cook for 1 to 2 minutes just to remove that raw flour taste. Season with salt and pepper.
Add the broth, heavy cream and Dijon mustard.
Cook, stirring occasionally, for 20 minutes.
Next, stir in the cheddar until it melts and fully incorporates.
Taste for seasoning, adding more salt and/or pepper if necessary.
Top with additional cheddar and parsley, if desired.