Step 1

Melt butter in a stock pot over medium heat. Add the carrots and the onion and sauté until tender, 4 to 5 minutes. Whisk in the flour and continue to stir for about 5 minutes. Slowly add the half and half and continue to stir until smooth. Pour in the vegetable broth and stir until well blended. Add the salt, pepper and the garlic.

Step 2

Reduce the temperature to medium low and simmer until mixture thickens, about 8 to 10 minutes.

Step 3

Add the broccoli and simmer until tender, about 15 minutes. Add the cheese and cook until cheese is melted, 4 to 5 minutes.