5 1/2 Tbsp butter , divided
1 1/3 cups chopped carrots (about 3)
1 cup chopped celery (2 stalks)
1 cup chopped yellow onion (1 small)
2 cloves garlic, minced
3 cups low-sodium chicken broth
3 1/2 cups peeled and cubed russet potatoes , cut 1/2-inch to 3/4-inch thick (2 large)
3 cups chopped broccoli florets (from about 2 heads)
1/4 tsp dried thyme Salt and freshly ground black pepper
6 Tbsp all-purpose flour
3 cups milk (preferably 1% or 2%)
1/2 cup heavy cream
2 cups shredded sharp cheddar cheese (8 oz)
1/3 cup finely shredded Parmesan cheese (1 oz)
In a large pot over medium heat, melt 1 1/2 Tbsp of the butter. Add carrots, celeryandonionandsaute3-4 minutes.Addgarlicandsaute30seconds longer.
Stir in chicken broth, potatoes and thyme and season with salt and pepper to taste. Bring to a boil over medium-high heat, then reduce heat to medium, coverwithlidandcook15minutes.Stirinbroccoliandcook5minutes longer or until veggies are tender.
Meanwhile, melt remaining 4 Tbsp butter in a medium saucepan over medium heat. Stir in flour and cook, whisking constantly for 1 minute.
While whisking vigorously, slowly pour in milk (whisk well until no lumps remain).
Cook stirring constantly until mixture begins to gently boil and thicken, stir in heavy cream. Remove from heat and once all veggies are tender pour into the soup and stir. Remove from heat and stir in cheddar and Parmesan cheese until melted. Serve warm.