01 - If using fresh peppers, roast red bell peppers over an open flame or under a broiler until skins are blackened on all sides. Transfer to a bowl, cover tightly, and let steam for 10 minutes. Remove charred skins, seeds, and stems, then chop the flesh.
02 - Heat olive oil in a large pot over medium heat. Add diced onion and cook until soft and translucent, about 5 minutes. Add minced garlic and cook for 1 minute until fragrant, being careful not to burn it.
03 - Stir in the roasted red peppers and smoked paprika; cook for 2 minutes to develop flavors. Pour in vegetable broth and bring to a simmer. Cook for 15 minutes to allow vegetables to soften and flavors to meld.
04 - Remove pot from heat. Use an immersion blender to puree the soup until completely smooth and velvety. Alternatively, transfer in batches to a countertop blender, pureeing carefully with hot liquids.
05 - Return the pureed soup to low heat. Stir in whole milk and heavy cream; heat gently until just steaming—do not let it come to a boil. Gradually add shredded smoked Gouda cheese, stirring constantly until fully melted and incorporated. Season with additional salt and pepper to taste.
06 - Ladle hot soup into serving bowls. Garnish with chopped fresh parsley and additional shredded Gouda cheese if desired. Serve immediately while hot.