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 the minced garlic and cook for 1 minute until fragrant, being careful not to burn it.
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 thoroughly to combine all ingredients.
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 it to the pot. Discard the bay leaf. Taste the soup and adjust salt as needed.
06 - For a smoother consistency, lightly mash some of the peas against the side of the pot with a spoon or use an immersion blender for a partially pureed texture. Leave some chunks for heartiness.
07 - Ladle the hot soup into bowls, garnish with fresh chopped parsley, and serve immediately with crusty bread if desired.