1. Preheat a grill to hot. Pierce the eggplant several times with a fork or a knife (otherwise the eggplant will explode when cooking, or as they like to say at work, “they become the suicide bombers of food.”). Roast the eggplant on all sides until the skin has blackened and charred completely (This may also be done by broiling the eggplant in the oven, but it will not taste quite as good.). Set aside to cool slightly. While still warm, cut off the top of the eggplant and make a vertical slit down the base of the eggplant. Using a spoon, scoop out the flesh and place in a colander for about half an hour to drain any excess liquid. Transfer to a bowl and mash up the eggplant with a fork.
2. Peel the potatoes and cut into quarters. Place in a large pot and cover completely with cold water and bring to a boil. Lower the heat to a simmer and cook until the potatoes are tender, about 20 minutes or so. The potatoes will be done when you pierce them with a knife and the potato falls off the knife. Using a ricer/food mill, puree the potatoes back into the pot you cooked them in.
3. Meanwhile, place the butter, milk, salt, and nutmeg in a saucepan and cook until the milk is steaming and the butter has completely melted. Add to the potatoes, along with the eggplant pulp, and stir gently until smooth and combined. Serve immediately.