Preheat the oven to 425°. Place the garlic on a sheet of foil; drizzle with EVOO. Season with salt and pepper, top with the rosemary and wrap in the foil, crimping the edges to seal. Roast until tender, 40 to 45 minutes. Let cool. Squeeze the soft, roasted cloves out onto a work surface. Using the flat side of a large knife, mash the garlic into a smooth paste.
While the garlic is roasting, place the potatoes and the parsnips in two separate medium pots; cover with cold water by 1 inch. Bring each to a boil over high heat. Salt the water, reduce the heat to medium and simmer until tender, about 10 minutes for the potatoes and 15 minutes for the parsnips. Drain.
Combine the vegetables in one pot. Add 3/4 cup milk, the butter and garlic paste; season with salt and pepper. Mash until smooth. Add the remaining 1/4 cup milk if too dry. Add the cheese and nutmeg; stir until melted. Season.