Step 1

Heat butter (or oil) in a large stockpot over medium-high heat until melted.  Add onion and carrots and sauté for 5 minutes, stirring occasionally, until the onion is translucent.  Stir in the garlic and sauté for an additional 1-2 minutes, stirring occasionally, until fragrant.  Stir in the flour and sauté for an additional 1 minute, stirring occasionally.

Step 2

Stir in the chicken stock until it is evenly combined.  Stir in the milk and mustard until combined.  Continue cooking until the soup, stirring occasionally, until it reaches a simmer.  Reduce heat to medium.  Add in the broccoli and cheddar, and stir until combined.  Continue cooking for 2-4 more minutes, or until the broccoli reaches your desired level of tenderness.

Step 3

Serve immediately, garnished with extra shredded cheese if desired.