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. Sauté for 5–7 minutes until vegetables are softened and fragrant.
02 - Stir minced garlic into the pot and cook for 1 minute until fragrant, 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 to combine thoroughly.
04 - Bring the mixture to a boil, then reduce heat to low. Simmer uncovered for 1 to 1.5 hours, stirring occasionally to prevent sticking, until peas are completely tender and soup has thickened considerably.
05 - Remove the ham hock if used, shred any meat from the bone, and return the shredded meat to the pot. Discard the bay leaf.
06 - Taste the soup and adjust salt as needed. For a smoother texture, lightly mash some peas against the pot side with a spoon or use an immersion blender for a partially pureed consistency.
07 - Ladle hot soup into bowls, garnish with chopped fresh parsley, and serve immediately.