Heat the olive oil in a large pot over medium heat. Add the lamb cubes and brown them on all sides for about 6 minutes. Remove the lamb and set it aside.
Add the onion to the same pot and cook until it softens, about 4 minutes. Stir in the garlic and cook for 1 minute more.
Return the lamb to the pot. Stir in the whole grain mustard and thyme until the meat is coated.
Pour in the broth and bring the mixture to a simmer. Add the parsnip chunks, then cover and cook on low heat for 1 hour and 15 minutes, stirring occasionally.
Season with salt and black pepper. Continue simmering uncovered for another 15 minutes until the parsnips are tender and the broth has thickened slightly.
Ladle into bowls and sprinkle with the chopped fresh parsley before serving.