Step 1

Prepare vegetables by grating or chopping. Shred cheese and set aside to allow it to come to room temperature.

Step 2

Add vegetable broth to a large soup pot over medium heat. Add the carrots, celery and potatoes, cover pot, and bring to a boil. Once boiling, reduce heat and simmer until the vegetables are tender, 3-5 minutes.

Step 3

Add chopped broccoli and simmer for another minutes or two, depending on how chunky or fine you chopped it. Remove from heat.

Step 4

In a separate skillet over medium heat, sauté onion in 1 tablespoon butter until tender and lightly browned.

Step 5

Add onion to pot with vegetables. Add remaining 4 tablespoons of butter to the skillet, over medium heat. Once melted, whisk in ¼ c. flour and stir well to make a roux.

Step 6

Add the half and half and milk, one cup at a time, stirring constantly. Cook roux, stirring continually with whisk until thickened, smooth and bubbly. Season well with salt and pepper.

Step 7

Slowly add rue to the pot of cooked vegetables, stirring carefully to combine. Cook for 2 minutes.

Step 8

Remove from heat and add grated cheese, stirring until melted. Taste and season with additional salt and pepper or vegetable bouillon base, to taste, if needed.