Step 1

Melt the butter in a large pot or Dutch oven over medium heat. Add the onion, salt, and several grinds of pepper and cook, stirring, for 5 minutes, or until softened. Stir in the garlic and cook for another minute, then sprinkle in the flour and whisk continuously for 1 to 2 minutes, or until the flour turns golden. Slowly pour in the milk, whisking continuously.

Step 2

Add the broth, broccoli, carrot, and mustard and stir to combine. Simmer for 15 to 20 minutes, or until the broccoli is tender.

Step 3

Gradually add the cheese, stirring after each addition, until all the cheese is melted and the soup is creamy. Season to taste and serve with croutons, if desired.