Heat the olive oil in a large pot over medium heat. Add the onion and garlic and cook until the onion softens.
Stir in the potatoes, carrots, parsnip, and turnip. Cook for 3 minutes, stirring occasionally.
Add the diced tomatoes, fish stock, and saffron threads. Bring the mixture to a simmer and cook for 15 minutes until the root vegetables are just tender.
Season the broth with salt and black pepper. Gently add the fish chunks and simmer for 5 to 7 minutes until the fish flakes easily.
Remove the pot from heat and stir in the chopped parsley before serving.