01 - If not using jarred roasted peppers, char fresh red bell peppers over an open flame or under the broiler until skins are blackened on all sides. Transfer to a bowl, cover tightly, and let steam for 10 minutes. Remove skins, seeds, and stems, then chop the peppers.
02 - Heat olive oil in a large pot over medium heat. Add diced onion and cook, stirring occasionally, until soft and translucent, approximately 5 minutes. Add minced garlic and cook for 1 minute until fragrant.
03 - Stir in the roasted red peppers and smoked paprika. Cook for 2 minutes to meld the flavors.
04 - Pour in vegetable broth and bring to a gentle simmer. Cook for 15 minutes to allow the flavors to develop.
05 - Remove pot from heat. Use an immersion blender to puree until completely smooth, or transfer in batches to a countertop blender.
06 - Return the pureed soup to low heat. Stir in whole milk and heavy cream; heat gently until just steaming, taking care not to boil. Gradually whisk in shredded smoked Gouda, stirring constantly until fully melted and smooth. Season with salt and pepper to taste.
07 - Ladle hot soup into serving bowls. Garnish with chopped fresh parsley and additional shredded Gouda cheese if desired.