Cheddar Vegetable Soup

This is one of my favorite comfort soups.  Don't let the title fool you because you can barely taste the vegetables with all the yummy cheesiness.
Veggie Base:
*1 TBSP. unsalted butter
*1 carrot, julienned*
*1/2 onion, diced
*1 celery stalk, diced
*1 potato, peeled and cubed (1/2")
*2 1/2 c. chicken (or vegetable) broth
Cheesy Mixture:
*3 TBSP. unsalted butter
*4 TBSP. flour
*1/2 tsp. ground dry mustard
*1/2 tsp. ground pepper
*2 c. milk (if you're feeling naughty replace 1/4 c. with heavy cream)
*2 c. cheddar cheese, grated
*2 TBSP. flour

In a stock pot heat 1 TBSP. butter over medium heat.  Add carrot, onion, celery and saute for about 2 minutes.  Add broth and potato, simmer about 15 minutes, until potatoes are soft.

Meanwhile, in a small saucepan, heat 3 TBSP. butter over medium-low heat, whisk in flour and dry mustard and continue whisking until flour is cooked through and mixture forms a thick paste.  Add pepper and milk(cream), increase heat to medium/medium-high and cook, stirring, until mixture gets thick (can take 5-10 minutes).  When it is thick, slowly whisk it into the vegetable soup pot.  Stir to combine well and continue to thicken.  Toss grated cheese with 2 TBSP. flour (this will keep the cheese from being grainy/stringy).  Remove soup from heat and slowly add cheese while stirring.