01 - If not using jarred peppers, 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. Add garlic and cook 1 minute, until fragrant.
03 - Stir in roasted red peppers and smoked paprika; cook 2 minutes to develop flavor.
04 - Pour in vegetable broth, bring to a simmer, and cook for 15 minutes to allow flavors to meld.
05 - Remove from heat. Use an immersion blender or transfer in batches to a blender to puree until completely smooth.
06 - Return to low heat. Stir in milk and heavy cream; heat gently until just steaming. Gradually add shredded Gouda, stirring until melted and smooth. Season with salt and pepper to taste.
07 - Ladle into bowls and garnish with chopped parsley and extra shredded Gouda if desired.