In a cast iron skillet over medium heat, melt the butter and cook the bacon until browned and crisp. Push the bacon to the edge of the pan and place the radishes cut side down into the skillet. Cook without stirring for 3 minutes, or until browned on the bottom. Add the shallots to the pan and continue to cook, stirring, another 2 minutes. Add the balsamic vinegar and water. Season generously with salt and pepper. Cover the pan, turn the heat down to low, and simmer for 6 minutes or until the radishes are tender (cooking time will depend on the size of your radishes). Remove the lid and allow to simmer 2 minutes longer, or until the juices thicken. Sprinkle with parsley and taste for seasoning. Add more salt and pepper as needed to taste.