Position rack in lower third of oven; preheat to 450°F (230°C).

Toss parsnips, pears, onion, oil, 1/2 teaspoon salt and pepper in a roasting pan. Roast, stirring every 10 minutes, until very soft and starting to brown, about 40 minutes.

Meanwhile, boil vinegar in a small saucepan until syrupy and reduced to about 1/4 cup, 10 to 14 minutes. (Watch the syrup carefully during the last few minutes of reducing to prevent burning.) Remove from the heat.

Purée half of the parsnip mixture with broth in a blender until very smooth; transfer to a large saucepan. Purée the other half with milk until very smooth. Add to the saucepan and stir in the remaining 1/2 teaspoon salt. Reheat the soup over medium heat, stirring often, about 5 minutes. Gently reheat the balsamic syrup if it has become thicker than syrup while standing. Ladle the soup into bowls and drizzle with the balsamic syrup.