01 - If using fresh peppers, roast them over an open flame or under a broiler until the skins are blackened and blistered. Transfer to a bowl, cover with plastic wrap, and let steam for 10 minutes. Peel off the charred skins, remove the seeds and stems, then chop the flesh into rough pieces.
02 - Heat olive oil in a large pot over medium heat. Add the diced onion and cook, stirring occasionally, until soft and translucent, about 5 minutes. Add the minced garlic and cook for 1 minute until fragrant, being careful not to brown it.
03 - Add the chopped roasted red peppers and smoked paprika to the pot. Stir well to combine and cook for 2 minutes, allowing the spices to bloom and the peppers to release their oils.
04 - Pour in the vegetable broth and bring to a gentle simmer. Reduce heat to low and cook for 15 minutes, allowing the flavors to meld together.
05 - Remove the pot from heat. Use an immersion blender to puree the soup until completely smooth and velvety. Alternatively, transfer the soup in batches to a countertop blender and blend until smooth, being cautious with hot liquids.
06 - Return the pureed soup to low heat. Stir in the whole milk and heavy cream, heating gently until the mixture is just steaming—do not let it boil. Gradually add the shredded smoked Gouda cheese, a handful at a time, stirring constantly until melted and fully incorporated.
07 - Taste the soup and season with salt and freshly ground black pepper as needed. Ladle into warm bowls and garnish with chopped fresh parsley and additional shredded Gouda cheese. Serve immediately while hot.