01 - Heat olive oil in a large soup pot or Dutch oven over medium heat. Add onion, carrots, celery, and a pinch of salt. Cook 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 it.
03 - Add diced potato, split peas, bay leaf, thyme, black pepper, smoked paprika, and ham hock (if using). Pour in broth and stir thoroughly to combine all ingredients.
04 - Bring mixture to a boil, then reduce heat to low. Simmer uncovered for 1–1.5 hours, stirring occasionally, until peas are completely tender and soup has thickened nicely.
05 - Remove ham hock if used, shred meat from bone, and return shredded meat to pot. Discard bay leaf.
06 - Taste and adjust salt as needed. For smoother texture, lightly mash some peas with spoon or use immersion blender for partial puree.
07 - Ladle hot soup into bowls, garnish with fresh parsley, and serve immediately.