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 Melt 1 tablespoon butter in a skillet over medium-high heat. Add onion; cook and stir until tender and translucent, about 5 minutes. Set aside. 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. Gradually add milk while whisking constantly; stir in chicken stock and bring to a simmer. Cook until mixture is thickened, about 20 minutes. Add broccoli, carrots, celery, and sautéed onion; simmer until all the vegetables are tender, about 15 minutes. Stir in Cheddar cheese until melted; season with salt and pepper to taste before serving.