Cheesy Chicken Broccoli Soup (Creamy Stovetop Dinner)

Ingredients

• 3 tablespoons (42 g) unsalted butter
• 1 medium yellow onion, finely chopped
• 1 medium carrot, finely diced
• 3 cloves garlic, minced
• 1/4 cup (30 g) all-purpose flour
• 5 cups (1.2 L) low-sodium chicken broth
• 1 1/2 lb (680 g) boneless skinless chicken breasts
• 1 teaspoon kosher salt, plus more to taste
• 1/2 teaspoon black pepper
• 1/2 teaspoon smoked paprika
• 5 cups (450 g) small fresh broccoli florets
• 1 cup (240 ml) half-and-half
• 1 teaspoon Dijon mustard
• 2 cups (225 g) freshly shredded sharp cheddar cheese
• 1/4 cup (25 g) grated Parmesan cheese
• Sliced scallions or extra cheddar, for serving optional