01 - Heat olive oil in a large pot over medium heat. Add onion, carrots, and celery; cook for 6 to 8 minutes, stirring occasionally, until softened.
02 - Stir in garlic and cook for 1 minute, until fragrant.
03 - Add split peas, vegetable broth, water, thyme, bay leaf, smoked paprika, black pepper, and salt. Mix thoroughly.
04 - Bring mixture to a boil. Reduce heat to low, cover, and simmer for 50 to 60 minutes, stirring occasionally, until peas are tender and soup is thickened.
05 - Remove bay leaf. For a velvety texture, use an immersion blender to partially or fully purée the soup as preferred.
06 - In a small bowl, whisk sour cream with milk or water until smooth and pourable. Transfer to a piping bag or small zip-top bag with a small corner snipped.
07 - Ladle soup into bowls. Pipe concentric circles of sour cream on each portion. Drag a toothpick or skewer from the center outwards to create a spiderweb motif. Sprinkle with fresh chives or parsley, if desired, and serve warm.