Melt the 2 tablespoons of unsalted butter in your large pot over medium heat. Add the finely diced onion and sliced carrots. Cook gently for about 5-7 minutes until onions are translucent and carrots have softened slightly.
Pour in 4 cups of low sodium chicken broth, then add the small broccoli florets. Stir in garlic powder, sea salt, black pepper, and thyme. Bring to a gentle boil, then reduce heat to a simmer. Cover and cook for about 15 minutes until broccoli is tender but still bright green.
In a small bowl, whisk together 3 tablespoons of all-purpose flour with a few tablespoons of cold water until smooth. Slowly stir this slurry into the simmering soup to thicken it. Cook, stirring regularly, for 5 more minutes until soup thickens and becomes creamy.
Lower heat and stir in heavy whipping cream and 1 teaspoon Dijon mustard. Gradually add shredded sharp cheddar cheese and parmesan cheese, stirring constantly until melted and fully incorporated. Adjust seasoning with salt or pepper if needed.
While soup simmers, slice off tops of bread loaves and hollow out the insides, leaving about a half-inch thick shell. Toast bread bowls in a 350°F oven for about 10 minutes if desired for extra crispiness.
Ladle the hot broccoli cheese soup into each bread bowl. Top with additional shredded cheddar cheese. Serve immediately and enjoy.
