01 - If using fresh peppers, roast 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. Peel away 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, stirring occasionally, 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 allow the flavors to meld. Pour in the vegetable broth, increase heat to bring to a simmer, then reduce to maintain a gentle simmer for 15 minutes.
04 - Remove the pot from heat. Using an immersion blender, puree the soup directly in the pot until completely smooth. Alternatively, transfer the soup in batches to a countertop blender, pureeing until silky and returning each batch to the pot.
05 - Return the pureed soup to low heat. Stir in the whole milk and heavy cream, heating gently until just steaming—do not let the mixture come to a boil. Gradually add the shredded smoked Gouda, stirring continuously until melted and fully incorporated. Season with additional salt and pepper to taste.
06 - Ladle the hot soup into serving bowls. Garnish with chopped fresh parsley and additional shredded Gouda cheese if desired. Serve immediately while hot.