01 - Heat olive oil in a large pot over medium heat. Add diced onion, carrots, and celery, and sauté for 6 to 8 minutes until vegetables soften.
02 - Stir in minced garlic and cook for 1 minute until fragrant.
03 - Add split peas, vegetable broth, water, dried thyme, bay leaf, smoked paprika, black pepper, and salt. Stir thoroughly to combine.
04 - Bring mixture to a boil, then reduce heat to low. Cover and simmer for 50 to 60 minutes, stirring occasionally, until the peas are tender and soup is thickened.
05 - Remove bay leaf. If a smoother texture is desired, use an immersion blender to partially or fully purée the soup.
06 - In a small bowl, whisk sour cream with a small amount of milk or water until it reaches a pourable consistency. Transfer to a piping bag or a small zip-top bag with a snipped corner.
07 - Ladle soup into bowls. Pipe sour cream in concentric circles atop each serving, then drag a toothpick or skewer from the center outward to create a spiderweb pattern.
08 - Garnish with freshly chopped chives or parsley if desired. Serve warm.