Cheddar Broccoli Potato Soup

Ingredients

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