Pour the vegetable broth into a medium saucepan and bring to a boil over high heat. Reduce heat to low, then cover.

Melt 4 tablespoons of the butter in a large, heavy saucepan over medium heat. Add the onion and sauté until translucent, about 10 minutes, stirring often. Add the parsnips and 3 teaspoons of the rosemary, and cook until parsnips start to brown, 8-10 minutes, stirring occasionally. Stir in the rice and continue to stir for 2 minutes. Pour in warm broth to cover, and simmer until almost all the broth is absorbed, about 6 minutes, stirring occasionally. Add more broth 1 cup at a time, allowing the broth to be absorbed before adding the next cup and stirring frequently, and cook until rice and parsnips are tender, about 20 minutes total. Remove from heat and stir in the last tablespoon of butter, the last 2 teaspoons of rosemary, and Parmesan. Season to taste with salt and pepper.

Serve hot, drizzling each serving with a little balsamic vinegar.