Position rack in lower third of oven; preheat to 450 degrees F.

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.

Puree half of the parsnip mixture with broth in a blender until very smooth; transfer to a large saucepan. Puree 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.

Remove the fibrous, woody core of parsnips before using: quarter parsnip lengthwise and cut out the core with a paring knife.