Heat the olive oil in a large Dutch oven over medium heat. Add the pork cubes and cook until lightly browned on all sides, about 5 minutes. Remove the pork to a plate and set aside.
Add the onion to the same pot and cook until softened, about 3 minutes. Stir in the garlic and cook for 30 seconds more.
Return the pork to the pot. Add the sweet potatoes, parsnips, carrots, chicken broth, thyme, salt, and pepper. Stir to combine.
Bring the mixture to a boil, then reduce the heat to low. Cover and simmer for 25 minutes, or until the vegetables are tender and the pork is cooked through.
Taste and adjust salt and pepper if needed. Sprinkle with fresh parsley just before serving.