Melt butter in a pot.

Add onion and sauté until onions are tender.

Stir in flour and salt and gradually add milk while stirring constantly.

When the mixture has begun to boil and thicken slightly, add the broth, broccoli, and carrots.

Heat over low heat for about 25 minutes, being careful not to let the soup boil; stir occasionally so vegetables don’t stick to the bottom of the pot.

Add salt and pepper to taste, and serve.