01 - In a large soup pot or Dutch oven, heat olive oil over medium heat. Add onion, carrots, celery, and a pinch of salt. Sauté for 5–7 minutes until softened.
02 - Stir in the garlic and cook for 1 minute until fragrant.
03 - Add the diced potato, split peas, bay leaf, thyme, black pepper, smoked paprika, and ham hock (if using). Pour in the broth and stir to combine.
04 - Bring the mixture to a boil, then reduce heat to low. Simmer uncovered for 1–1.5 hours, stirring occasionally, until peas are tender and soup has thickened.
05 - Remove the ham hock (if used), shred any meat, and return it to the pot. Discard the bay leaf.
06 - Taste and adjust salt as needed. For a smoother texture, lightly mash some of the peas with a spoon or use an immersion blender for a partially pureed soup.
07 - Ladle into bowls, garnish with fresh parsley, and serve hot.