Make the base for the soup: Melt the butter in a large pot over medium-high heat. Toss in the diced onion and saute in the butter for 4 minutes or until they have turned translucent. Add the minced garlic to the pot and saute with the onion for another 2 minutes. Finally, add in the flour and stir so that it combines with the butter to form a paste. Continue to stir everything for another couple of minutes.

Cook the broccoli: Slowly pour the stock into the pot and stir so that the flour paste is thoroughly incorporated into the liquid (no lumps!). Then add the half & half, chopped pieces of broccoli, peeled carrot, salt, pepper, paprika, mustard powder, and nutmeg. Stir these ingredients together and let the liquid come to a boil. Then lower the heat and let everything simmer for 15 to 20 minutes or until the broccoli is tender.

Finish the soup: Keep the heat on low and toss in the shredded cheddar cheese. Stir the soup so that the cheese melts into the broth. Finally, taste the soup and add additional salt and pepper to your liking.

Ladle the soup into individual bowls and enjoy!