Heat the olive oil in a skillet over medium heat, then add the sausage, breaking it apart with a spatula. Cook until browned and fragrant, about 5–7 minutes. Transfer the cooked sausage to the slow cooker.
Place the chopped parsnips, turnips, and diced onion into the slow cooker, pairing with the browned sausage for a hearty base. Toss in the minced garlic and sprinkle with cinnamon and nutmeg if using.
Pour the vegetable broth over all the ingredients, ensuring they are mostly submerged. Cover the slow cooker with its lid and set to low. Let it simmer for 6 hours until the vegetables are tender and flavors meld.
Once cooking is complete, uncover the slow cooker and gently stir to combine the ingredients. Taste and adjust seasoning with salt and pepper as desired. The soup should have a rich, comforting aroma and a thick, velvety texture.
Ladle the hot soup into bowls, garnishing with fresh herbs or a drizzle of olive oil if desired. Serve alongside crusty bread for a full seasonal meal.
