Pre-heat the oven to 425°F.
Drizzle the exposed cloves of garlic with olive oil, season with salt and pepper and wrap in a foil pouch. Roast for about 40 minutes until very soft and tender and caramel in color. Cool to handle.
For the filling, heat the olive oil, two turns of the pan, in a Dutch oven or heavy pot over medium high heat. Add the guanciale or pancetta and lightly brown, 2 minutes, then add the beef and caramelize, browning the meat to develop the sugars. Add salt and pepper and the carrots, celery, onion and 1 bulb of roasted garlic, squished from the skins. Stir well to incorporate the garlic; add the bay and herb bundle and partially cover. Cook for 10-12 minutes to soften, stirring occasionally, over medium heat. Stir in the tomato paste until fragrant, 1-2 minutes, then add the wine, stock and 1 cup milk. Bring to a bubble; reduce the heat and simmer gently.
Meanwhile, cover the potatoes with water in another pot. Bring to a rolling boil, then salt the water and cook to tender. Drain, then pass the potatoes through a ricer. Add the remaining milk, roasted garlic, 1 cup grated cheese, salt, pepper and nutmeg; combine and taste to adjust the seasoning, then mix in the egg yolks.
Pre-heat the broiler and place the rack in the center of the oven.
Transfer the beef filling to a casserole or individual bowls. Pipe or spread the potatoes over top of the beef and sprinkle with the remaining cheese; broil to brown and serve. Garnish with parsley.