In a soup pot, cook the bacon over medium-high heat until crisp, about 5 minutes. Transfer to a cutting board and finely chop. Spoon off all but a few tablespoons of the drippings. Melt the butter in the bacon drippings, then reduce the heat to medium. Stir in the potatoes, parsnips, onion, garlic and nutmeg. Season with pepper and add the parsley. Partially cover and cook, stirring occasionally, until the vegetables soften, 15 to 20 minutes. Discard the parsley.
Working in batches if necessary, puree the vegetable mixture with the chicken stock in a food processor or blender (or add the stock to the soup pot and use an immersion blender). Stir in the cream and bacon bits; season with salt and pepper. Ladle the soup into bowls, then sprinkle with pepitas and chives. Serve with toasted, buttered English muffins for dunking.