Broccoli-Cheese Soup

This is my version of the original from The New Southern Garden Cookbook. Other than the cheese, which is the primary protein source, this is a pretty healthful soup. (Crumbled bacon would be a delicious addition.) It's different from other recipes I’ve had for this soup in that the veggies are pretty chunky and it includes potato, which contributes creaminess.
2 Tbsp. butter
1 onion, chopped
1 carrot, chopped
1 celery rib, chopped
1 small potato, cut into chunks
2 broccoli crowns, cut into florets and then chop the stalks
Salt and pepper
1/4 cup all-purpose flour
2 cups chicken or vegetable broth
1 tsp. dried or 1 Tbsp. fresh thyme
1 1/2 tsp. dried mustard
2 cups milk
1 1/2 cup grated white cheddar or cheddar cheese
2 tsp. cornstarch

1. Melt butter in Dutch oven; add in onions and next 4 ingredients. Sauté 10 minutes or until vegetables begin to soften. Season with salt and pepper. Stir in flour, and cook 1 minute. Gradually add in broth, and cook until thickened. Stir in thyme, dried mustard, and milk. Simmer for 25 minutes or until potatoes and broccoli are tender.
2. Toss cheese with cornstarch; stir into soup. Season with salt and pepper to taste. Simmer 5 more minutes or until cheese is melted and thoroughly heated. Serve immediately.