01 - Place whole red bell peppers on a baking sheet and broil or roast at 450°F until skins are charred, turning occasionally (about 15 minutes). Transfer to a bowl, cover, and let steam for 10 minutes. Peel off skins, remove seeds, and chop the flesh.
02 - In a large pot, melt the butter over medium heat. Add the onions and cook until translucent, about 5 minutes. Add garlic and cook for another minute until fragrant.
03 - Add the chopped roasted red peppers, smoked paprika, salt, pepper, and cayenne (if using). Stir to combine and cook for 1-2 minutes to meld flavors.
04 - Pour in the vegetable broth. Bring to a boil, then reduce heat and simmer for 15 minutes to allow flavors to develop.
05 - Use an immersion blender to puree the soup until smooth, or transfer to a standard blender in batches, being careful with hot liquid.
06 - Stir in the heavy cream and shredded Gouda cheese. Heat gently over low heat, stirring continuously, until the cheese melts completely and the soup reaches a creamy, smooth consistency. Adjust seasoning if needed.
07 - Ladle the hot soup into bowls. Garnish with finely chopped fresh chives or parsley and extra shredded Gouda cheese, if desired.