01 - Heat olive oil in a large soup pot or Dutch oven over medium heat. Add onion, carrots, celery, and a pinch of salt. Sauté for 5–7 minutes until softened and fragrant.
02 - Stir in minced garlic and cook for 1 minute until fragrant, being careful not to burn.
03 - Add diced potato, rinsed split peas, bay leaf, dried thyme, black pepper, smoked paprika, and ham hock (if using). Pour in broth and stir everything to combine thoroughly.
04 - Bring mixture to a boil, then reduce heat to low. Simmer uncovered for 1–1.5 hours, stirring occasionally to prevent sticking, until peas are completely tender and soup has thickened nicely.
05 - Remove ham hock if used. Shred meat from bone and return to pot. Discard bay leaf.
06 - Taste soup and adjust salt as needed. For smoother texture, lightly mash some peas against side of pot or use immersion blender for partial puree.
07 - Ladle hot soup into bowls, garnish with fresh chopped parsley, and serve immediately.