Preheat your broiler and line a baking sheet with aluminum foil. Slice the red bell peppers in half and remove the seeds. Arrange them cut-side down, drizzle with olive oil and sprinkle with salt.

Roast the red bell peppers for 12–15 minutes under the broiler until blistered and charred. Turn occasionally for even charring. Remove and cover in a bowl to steam.

Allow the peppers to steam for about 10 minutes. Peel off the skins and chop them into bite-sized pieces.

Melt 3 tablespoons of butter in a Dutch oven over medium heat. Add diced yellow onion and sauté for 5-6 minutes until translucent.

Stir in minced garlic and cook for 1 minute until fragrant, being careful not to brown the garlic.

Sprinkle in 2 tablespoons of all-purpose flour and stir constantly for about 2 minutes to create a roux.

Gradually whisk in 4 cups of broth, ensuring no lumps remain. Stir in the roasted peppers, smoked paprika, thyme, and black pepper.

Bring the soup to a gentle boil, then simmer uncovered for 15 minutes. Stir occasionally.

Blend the soup until smooth using an immersion blender or in batches in a standard blender.

Return the soup to low heat and stir in shredded gouda, cooking until melted.

Taste and adjust seasoning. Stir in heavy cream if desired for added richness.

Ladle soup into bowls and garnish with fresh basil. Serve hot with grilled cheese croutons or crusty bread.