Preheat oven to 400° F.

Cut ¼” off the top of the head of garlic, making sure that all of the cloves are cut open and the root and bulb remain intact. Place garlic bulb on a double layer of foil, then drizzle the cut side of the garlic with olive oil.

Wrap the garlic up loosely with the foil and place it in a small oven-safe dish. Roast for about 35 minutes, or until the garlic is golden brown, softened, and fragrant. Set aside to cool.

Add the parsnips, potato, and 1 teaspoon salt to a medium saucepan. Add enough water to just barely cover the vegetables and then place the pan over high heat.

Bring the water to a boil and then reduce the heat to medium to medium-high. Boil for 17-20 minutes, or until the parsnips are fork tender.

Drain the water and return the vegetables to the pan. Add the remaining ½ teaspoon salt, pepper, half & half, butter, and thyme.

Squeeze the roasted garlic out of the skins and into the parsnip puree.

Use an immersion blender on low speed to mash the vegetables. Increase the speed of the blender and continue to puree until you reach your desired consistency. Blend as little or as much as you like, from a bit chunky to completely smooth.

Stir in the grated Parmesan and season with additional salt and pepper, if needed. Transfer to a serving dish, if desired. Sprinkle with additional fresh thyme leaves, if desired. Enjoy hot.