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