01 - Roast red peppers over an open flame or under a broiler until skins are blackened. Place in a bowl, cover, let steam 10 minutes, then peel, seed, and chop.
02 - In a large pot, heat olive oil over medium heat. Add onion and cook until soft and translucent, about 5 minutes.
03 - Add garlic and cook 1 minute, until fragrant.
04 - Stir in roasted red peppers and smoked paprika; cook 2 minutes.
05 - Pour in vegetable broth, bring to a simmer, and cook for 15 minutes.
06 - Remove from heat. Use an immersion blender (or transfer in batches to a blender) to puree until smooth.
07 - Return to low heat. Stir in milk and heavy cream; heat gently until just steaming (do not boil).
08 - Gradually add shredded Gouda, stirring until melted and smooth. Season with salt and pepper to taste.
09 - Ladle into bowls and garnish with parsley and extra Gouda if desired.