Before diving in, gather and prepare all your ingredients. Chop the broccoli, mince the onion and celery, and shred the cheese. This makes cooking smoother and more enjoyable.

In a large pot over medium heat, melt the butter. Once it's bubbly, add the flour, stirring continuously for about 2 minutes. The goal is to create a roux, and you want to cook it until it’s light golden brown. This step is key to achieving a thick, creamy soup.

Next, add the finely chopped onion and minced celery. Sauté until the onions become translucent and fragrant, usually about 3 to 4 minutes. This is where your kitchen fills with a heavenly aroma!

Slowly whisk in the chicken stock until smooth, followed by the whole milk. Bring this combination to a gentle simmer. Keep stirring to avoid any lumps. What you create here is a velvety broth that lays the foundation of your soup.

Once simmering, add the broccoli florets. Let them cook for about 5 minutes, or until they are tender but still vibrant in color. Remember, you want your broccoli to maintain some of its crunch for texture!

Off the heat, it’s time to stir in the sharp cheddar cheese. Do this gradually, allowing it to melt smoothly into the mix. This is where the soup gets its creamy nature. Stir in the garlic powder and smoked paprika for an extra flavor boost, along with salt and pepper to taste.

Ladle the soup into bowls. Top generously with additional shredded cheddar cheese. If you’re feeling fancy, sprinkle some chives or parsley on top for that extra pop. It not only looks great but also adds to the flavor!