1 Tbsp. Butter
¼ Cup melted butter
¼ Cup flour
2 Cups milk
2 Cups chicken stock
1-½ Cups coarsely chopped broccoli florets
1 Cup matchstick-cut carrots
1 Stalk celery, thinly sliced
2-½ Cups shredded sharp cheddar cheese
salt and ground black pepper to taste
Melt 1 Tbsp. butter in a skillet over medium-high heat. Saute onion in hot butter until translucent, about 5 minutes. Set aside.
Whisk ¼ melted butter and flour together in a large saucepan over medium-low heat; cook until flour loses it's granular texture, adding 1 to 2 Tbsps of milk if necessary to keep the flour from burning, 3 to 4 minutes.
Gradually pour milk into flour mixture while whisking constantly. Stir chicken stock into milk mixture. Bring to a simmer; cook until flour taste is gone and mixture is thickened, about 20 minutes. Add broccoli, carrots, sauteed onion, and celery; simmer until vegetables are tender, about 20 minutes.
Stir cheddar cheese into vegetable mixture until cheese melts. Season with salt and pepper to taste.