In a large pot over medium heat, melt the 2 tablespoons of unsalted butter. Add the finely diced onion and sliced carrots. Sauté for about 5-7 minutes until tender and translucent.
Pour in the 4 cups of low sodium chicken broth and add the broccoli florets. Bring to a simmer and cook for about 10 minutes until broccoli is tender but vibrant green.
Stir in the garlic powder, sea salt, black pepper, and thyme. Adjust seasoning to taste.
Sprinkle the 3 tablespoons of all-purpose flour over the soup and stir continuously for about 1 minute to thicken.
Reduce heat to low and stir in the 1/2 cup of heavy whipping cream and 1 teaspoon of Dijon mustard. Fold in the cheeses until melted and creamy.
Preheat your oven to 375°F (190°C). Hollow out bread rolls and place on a baking sheet. Bake for about 10-15 minutes until crispy and warm.
Ladle the soup into the bread bowls, garnish with additional cheese, and serve immediately.