Cheddar, Broccoli, and Potato Soup

5 1/2 tablespoons butter, divided
1 1/3 cups chopped carrots (about 3)
1 cup chopped yellow onion (about 1 small)
2 cloves garlic, minced
3 cups low-sodium chicken broth or vegetable broth
3 1/2 cups peeled and cubed russet potatoes, cut 1/2- to 3/4-inch thick (about 2 large)
3 cups chopped broccoli florets (from about 2 heads)
1/4 teaspoon dried thyme
Salt and freshly ground black pepper
6 tablespoons all-purpose flour
3 cups milk (preferably 1% or 2%)
1/2 cup heavy cream
2 cups shredded sharp cheddar cheese (about 8 ounces)
1/3 cup finely shredded parmesan cheese (about 1 ounce)

In a large pot over medium heat, melt 1 1/2 tablespoons butter.  Add carrots and onion, and saute for 3-4 minutes.  Add garlic and saute 30 seconds longer.

Stir in broth, potatoes, and thyme, and season with salt and pepper to taste.  Bring to a boil over medium-high heat, then reduce the heat to medium, cover with lid, and cook for 15 minutes.  Stir in broccoli and cook for 5 minutes longer, or until vegetables are tender.

Meanwhile, melt remaining 4 tablespoons butter in a medium saucepan over medium heat.  Stir in flour and cook, whisking constantly, for 1 minute.  While whisking vigorously, slowly pour in the milk, whisking well until no lumps remain.

Cook, stirring constantly, until mixture begins to gently boil and thicken, then stir in heavy cream.  Remove from heat, then pour into the vegetable soup and stir.  Remove from heat and stir in cheddar and parmesan cheeses until melted.  Serve warm.

Serves 6.

From CookingClassy.com, with minor change