Cook the bacon in a large, heavy pot over medium heat until crisp. Remove with a slotted spoon and set aside. In the remaining fat, cook the onion and flour until the onions are tender but not browned, about 5 minutes. Add the parsnips and potatoes, stirring to coat them well, and cook for 5 minutes.
Add the water, bring to a boil, and simmer covered until the parsnips are tender, 20 to 30 minutes.
Add the milk and spinach and bring to a boil. Adjust the seasoning with salt and pepper and serve garnished with bacon. Serves 6 to 8.