Toss parsnip, pears, onion, oil and 1/2 teaspoon salt in a roasting pan. Roast, stirring every 10 minutes, until very soft and starting to brown, about 40 minutes
Boil vinegar in a small saucepan until syrupy and reduced to about 1/4 cup, 10 to 15 minutes. Babysit the vinegar to ensure you do not burn it. Remove from heat.
Puree half the parsnip mixture with broth in a blender until smooth. Transfer to a large pot. Puree the second half of the parsnip mixture with the milk until very smooth. Add to the pot and stir in the remaining half teaspoon of salt.
Reheat the soup over medium heat, stirring often, about 5 minutes. If the balsamic syrup has become too thick, gently reheat.
Ladle the soup into bowls and drizzle with the balsamic syrup.