Melt butter in a pot and sauté onions until soft.
Sprinkle flour over the onions and cook, stirring, for 1-2 minutes.
Whisk in half & half and chicken stock. Bring to a boil, then reduce heat to medium.
Add broccoli and carrots, cooking on medium-low for 20-25 minutes until tender.
Season with salt and pepper to taste.
For a smoother soup, blend 1 cup of it and stir back into the pot.
Lower the heat and stir in cheese, ensuring the soup doesn’t overheat to avoid graininess.
Add nutmeg if desired and serve with crusty bread.