Cook onions and garlic in butter until fragrant and soft.
Pour in vegetable or chicken broth for a flavorful base.
Add chopped broccoli and simmer until tender and bright green.
Mix butter and flour in a pan to thicken the soup.
Stir roux into the soup, whisking to achieve a creamy consistency.
Gradually mix shredded cheddar until melted and smooth throughout.
Add salt, pepper, optional nutmeg, and serve hot with bread.