Preheat the oven's broiler to high and line a baking sheet with aluminum foil.

Place whole red bell peppers on the baking sheet, drizzle with olive oil, and sprinkle with kosher salt. Roast for 12-15 minutes, turning occasionally, until charred.

Transfer the roasted peppers to a heatproof bowl, cover tightly with plastic wrap, and let steam for 10 minutes.

Melt butter in a large pot over medium heat, add diced onion and cook for 5-6 minutes until soft; then stir in minced garlic and sauté for 1 more minute.

Sprinkle flour over the mixture, stirring to make a roux, and allow to cook for 1-2 minutes. Gradually whisk in broth.

Add chopped roasted peppers, smoked paprika, thyme, and black pepper, bringing to a gentle boil. Reduce to a simmer for 15 minutes.

Blend the soup until smooth and velvety using an immersion blender.

Return to low heat, gradually stir in shredded gouda until melted and creamy. Optional: stir in heavy cream for extra richness.

Stir in chopped basil before serving, then ladle soup into bowls and garnish with extra basil or a drizzle of cream. Serve with crusty bread or grilled cheese croutons.