Preheat your broiler to high and line a baking sheet with foil. Wash and dry the red bell peppers.

Coat the peppers lightly with olive oil and sprinkle with kosher salt. Broil for 12 to 15 minutes, turning frequently until charred.

Transfer the charred peppers to a bowl and cover to steam for 10 minutes. Peel off the skins, remove stems and seeds, and chop the peppers.

In a large pot, melt butter over medium heat. Add diced onion and sauté for 5 to 6 minutes until translucent.

Stir in minced garlic and cook for 1 minute. Add flour and stir for 2 minutes to create a roux.

Gradually whisk in broth, ensuring no lumps remain. Add roasted peppers, smoked paprika, thyme, and black pepper. Simmer for 15 minutes.

Use an immersion blender to blend the soup until smooth. Alternatively, transfer to a blender in batches.

Return pot to low heat and add gouda in batches, stirring until melted to achieve a thick consistency.

Taste and adjust seasoning as needed. Stir in fresh basil before serving. Serve warm with crusty bread or grilled cheese croutons.