Copycat Panera® Broccoli Cheddar Soup

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