01 - If not using jarred roasted peppers, char fresh red bell peppers over an open flame or under the broiler until skins are blackened and blistered. Transfer to a bowl, cover tightly, and let steam for 10 minutes. Remove skins, seeds, and stems, then chop the flesh.
02 - Heat olive oil in a large pot over medium heat. Add diced onion and cook, stirring occasionally, until soft and translucent, approximately 5 minutes. Add minced garlic and cook for 1 minute until fragrant.
03 - Stir in roasted red peppers and smoked paprika; cook for 2 minutes to meld flavors. Pour in vegetable broth, bring to a simmer, and cook for 15 minutes to allow peppers to fully soften.
04 - Remove pot from heat. Puree the mixture using an immersion blender until completely smooth, or transfer in batches to a countertop blender and blend until velvety.
05 - Return the pureed soup to low heat. Stir in whole milk and heavy cream; heat gently until just steaming. Do not allow to boil as this may cause the dairy to separate.
06 - Gradually add shredded smoked Gouda, stirring continuously until fully melted and incorporated. Season with additional salt and pepper to taste. Ladle into bowls and garnish with fresh parsley and extra Gouda if desired.