Preheat oven to 400ºF and cut off the top third of the whole head of garlic to expose cloves. Drizzle bulb with EVOO, wrap tightly in foil and roast to tender, 40-45 minutes.
Once garlic has been roasted, cover potatoes with water and bring to a boil. Salt water and cook to tender, 12-15 minutes. Drain potatoes and return to warm pot, add all of the roasted garlic and a half a cup of milk or half-n-half to start. Add butter and mash, stir in beaten egg, half of cheese, pepper and nutmeg, and mash to desired consistency. Add a splash more liquid if necessary, cover and reserve.