In a large saucepan over medium heat, melt ¼ cup of unsalted butter until bubbly. Add in the diced onion, sautéing for about 4 minutes until it turns translucent and fragrant.

Once the onion has softened, stir in 2 minced garlic cloves and sauté for an additional 30 seconds.

Sprinkle in ¼ cup of all-purpose flour, stirring well to combine. Cook this mixture for 1 minute.

Gradually whisk in 16 ounces of broth, followed by 16 ounces of whole milk. Add ½ teaspoon of salt, ½ teaspoon of paprika, and ¼ teaspoon of pepper.

Fold in the chopped broccoli and grated carrot, bringing the soup to a simmer and cooking for 10-12 minutes until tender.

Remove from heat and slowly stir in 8 ounces of freshly grated smoked gouda cheese, stirring until melted.

Ladle the warm soup into bowls and optionally garnish with garlic butter croutons.