In a large stockpot, melt the butter over medium-low heat. Add the onion and carrot and cook for about 5 minutes, or until the onion is tender. Sprinkle the vegetables with the flour and, stirring constantly, continue cooking for 3 minutes. Remove the pot from the heat and add the chicken stock. Add the squash, garlic, and parsley, and simmer, covered, for 45 minutes. Set aside to cool for 10 minutes. In a blender or food processor, purée the mixture until smooth, in batches. Return the soup to the pot, add the milk, cream, and syrup, stir to incorporate, and heat through. Garnish with parsley and black pepper.
Make Ahead: This soup can be prepared up to the purée stage, covered, and refrigerated for 4 days or frozen in an airtight container for 1 month. To use: For each serving, combine ½ cup of the thawed purée, 2 tablespoons of milk, 2 teaspoons of cream, and 1 teaspoon of maple syrup, then heat through.