01 - Heat olive oil in a large pot over medium heat. Add diced onion and sauté for 4–5 minutes until softened and translucent.
02 - Stir in minced garlic and cook for 1 minute, stirring frequently to prevent burning and release aromatic oils.
03 - Add roasted red peppers to the pot along with smoked paprika, cayenne pepper, salt, and black pepper. Cook for 2 minutes to toast the spices and meld flavors.
04 - Pour in vegetable broth and bring to a gentle simmer. Cook uncovered for 10 minutes to allow flavors to develop and concentrate.
05 - Remove from heat. Using an immersion blender, puree the soup until completely smooth and velvety. Alternatively, transfer carefully to a countertop blender in batches, venting lid to prevent steam buildup.
06 - Return soup to low heat if necessary. Gradually whisk in shredded Gouda cheese, adding a handful at a time and allowing each addition to fully melt before adding more.
07 - Pour in heavy cream while stirring continuously. Heat through gently until the soup reaches serving temperature. Adjust seasoning with additional salt or pepper as desired.
08 - Ladle hot soup into bowls and garnish with chopped chives or parsley and additional shredded Gouda if desired. Serve immediately while hot.