Heat the olive oil in a large pot over medium-high heat. Add the pork pieces and cook until browned on all sides, about 6 to 8 minutes.
Add the onion and garlic to the pot. Cook for 3 minutes until the onion starts to soften.
Stir in the smoked paprika, salt, and black pepper. Cook for 1 minute to toast the spices.
Add the carrots, parsnips, and potatoes. Stir to coat the vegetables with the spices.
Pour in the chicken broth and bring the mixture to a boil. Reduce the heat to low, cover, and simmer for 45 minutes until the pork and vegetables are tender.
Taste and adjust salt or pepper if needed. Ladle into bowls and sprinkle with fresh parsley before serving.