Step 1

Dice the onion. Chop the broccoli into very small pieces. Peel and slice the carrots.

Step 2

Add the butter and onion to a large soup pot and sauté over medium until the onions are soft and translucent. Add the flour and continue to sauté for about 2 minutes more, or until the flour is coating the bottom of the pot and is a light golden brown color.

Step 3

Add the chicken broth and whisk to dissolve all the flour off the bottom of the pot. Turn the heat up to medium-high and, while stirring often, allow the broth to come up to a simmer. When it reaches a simmer it will thicken to a gravy consistency.

Step 4

Turn the heat back down to medium and whisk in the milk, smoked paprika, garlic powder, black pepper, and cayenne pepper. Allow the broth to come back up to a simmer.

Step 5

Add the chopped broccoli and carrots, allow the broth to come back up to a simmer, and continue to simmer the vegetables, stirring often, for 15 minutes, or until the carrots are tender.

Step 6

Finally, turn the heat down to medium-low and stir the shredded cheese into the soup, one handful at a time, until it is fully melted. Taste the soup and add salt if needed (this will depend on the salt content of your broth—I did not add any).