Cheesy Vegetable Chowder

Name: Cheesy Vegetable Chowder
Ingredients: * 5 tbsp butter, divided; * 3 large carrot, chopped; * 3 stalk celery, chopped; * 1 yellow onion, diced; * 4 clove garlic, minced; * 4 c or a 32 oz box, low sodium chicken broth; * 3 russet potato, peeled and; * 1 celery root, peeled and; * 2 medium head broccoli, chopped into floret; * 1 small head cauliflower, chopped into floret; * 1/4 tsp dried thyme; * 1 tsp salt; * 1/2 tsp ground black pepper; * pinch paprika and cayenne pepper; * 6 tbsp all purpose flour; * 3 c milk (1%, 2% or whole); * 1/2 c 1/2 and 1/2 (non fat, low fat or regular); * 2 c shredded medium or sharp cheddar cheese (8 oz block)