Begin by melting the butter in a large pot over medium heat. Once the butter is melted and bubbling, add the chopped onion and diced celery. Sauté these until they become soft and translucent, which should take about 5 minutes. This step is essential as it builds the base flavor for your soup.

Once your vegetables are ready, sprinkle the flour over the mixture. Stir the flour in, cooking it for about 1 to 2 minutes. This helps to thicken the soup later. Gradually pour in the chicken stock while stirring continuously. This technique prevents lumps from forming. Bring this to a simmer, allowing the mixture to thicken slightly.

With your base now thickened, it’s time to add the broccoli florets. Stir them in along with the whole milk. Allow this to simmer for about 10 minutes until the broccoli becomes tender. It’s such a vibrant green at this stage that you’ll be tempted to dive in immediately.

Turn the heat down to low now, and gradually stir in the shredded cheddar. It’s like watching a masterpiece come together. Make sure to keep stirring until the cheese has fully melted and the soup becomes creamy. At this point, season with Dijon mustard, smoked paprika, salt, and freshly ground black pepper to taste. Sample it! You want the flavors to sing just right.

Finally, ladle the soup into bowls. Top with extra shredded cheddar for that cheesy goodness. You can also add a sprinkle of freshly cracked black pepper if you desire. Serve immediately, and watch your friends and family light up with joy.