Melt the butter in a large saucepan over medium heat until bubbly.

Add the diced onion and sauté until translucent, about 4 minutes. Stir in minced garlic and cook for an additional 30 seconds.

Sprinkle in all-purpose flour and stir constantly to create a roux, cooking for 1 minute.

Gradually whisk in the broth and milk, continuing until smooth and letting it reach a gentle simmer for 2-3 minutes.

Add salt, paprika, and pepper, stirring well to combine.

Fold in chopped broccoli and grated carrot. Cover and cook on low for 10-12 minutes.

Off the heat, gradually stir in shredded smoked gouda until melted.

Ladle into bowls and garnish with crispy croutons. Serve hot.