Preheat your broiler to high. Line a baking sheet with aluminum foil. Wash and cut the bell peppers in half, removing seeds.

Drizzle halved peppers with olive oil and sprinkle with kosher salt. Place skin-side up on the baking sheet and roast for 12-15 minutes.

Transfer roasted peppers to a covered bowl to steam for 5-10 minutes. Peel off charred skins, chop, and set aside.

Melt 2 tablespoons of butter in a large pot over medium heat. Add diced onion and sauté for 5-6 minutes until translucent.

Add minced garlic to the pot and cook for another minute, stirring constantly to prevent burning.

Sprinkle in 2 tablespoons of flour, whisking until combined. Cook for about 2 minutes to form a roux.

Gradually add 4 cups of broth, whisking continuously to avoid lumps. Bring to a gentle boil.

Stir in chopped roasted peppers, smoked paprika, thyme, and black pepper. Let it simmer for about 15 minutes.

Blend the soup until smooth using an immersion blender.

Return the soup to low heat and stir in 1 cup of shredded gouda until melted. Adjust seasoning as needed.

Optional: Stir in 1/2 cup of heavy cream before serving. Ladle soup into bowls and garnish with fresh basil. Add croutons or prosciutto if desired.