01 - If using fresh peppers, roast red bell peppers over an open flame or under a broiler until skins are blackened and blistered. Transfer to a bowl, cover tightly, and let steam for 10 minutes. Peel off charred skins, remove 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, stirring constantly to prevent burning.
03 - Stir in roasted red peppers and smoked paprika. Cook for 2 minutes to allow flavors to meld. Pour in vegetable broth and bring to a gentle simmer. Cook for 15 minutes to deepen the flavor profile.
04 - Remove pot from heat. Use an immersion blender to puree the mixture until completely smooth. Alternatively, transfer soup in batches to a countertop blender, blending until velvety. Return pureed soup to the pot.
05 - Place pot over low heat. Stir in whole milk and heavy cream, heating gently until just steaming. Do not allow to boil. Gradually add shredded smoked Gouda, stirring continuously until fully melted and incorporated. Season with salt and black 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.