1 tablespoon butter 
½ onion, chopped 
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
Step 1 Melt 1 tablespoon butter in a skillet over medium-high heat. Saute onion in hot butter until translucent, about 5 minutes. Set aside.
Step 2 Whisk 1/4 cup melted butter and flour together in a large saucepan over medium-low heat. Continue to whisk and cook , adding 1 to 2 tablespoons of milk if necessary to keep the flour from burning, 3 to 4 minutes.
Step 3 Gradually pour milk into flour mixture while whisking constantly. Stir chicken stock into milk mixture. Bring to a simmer; cook until mixture is thickened, about 20 minutes. Add broccoli, carrots, sauteed onion, and celery; simmer until vegetables are tender, about 20 minutes.
Step 4 Stir Cheddar cheese into vegetable mixture until cheese melts. Season with salt and pepper to taste.
Cook's Note: 
I use 2% milk but you can use any, including half and half.
Prep: 15 mins 
Cook: 50 mins 
Total: 1 hr 5 mins 
Servings: 8 
Yield: 8 servings 
Nutrition Facts 
Per Serving: 304 calories; protein 14.3g; carbohydrates 10.7g; fat 23g; cholesterol 70.5mg; sodium 624mg.