Heat the olive oil in a large pot over medium heat. Add the onion and cook until it softens, about 5 minutes. Stir in the garlic and cook for 1 minute more.
Add the carrots, parsnips, and potatoes to the pot. Stir to coat the vegetables with the oil and cook for 3 minutes.
Pour in the vegetable broth. Add the white beans, rosemary sprigs, salt, and black pepper. Bring the mixture to a boil, then reduce the heat to low.
Cover the pot and simmer for 25 minutes, or until the root vegetables are fork-tender. Remove the rosemary sprigs before serving.
Ladle the stew into bowls and top each serving with chopped fresh parsley.