For the preserved mushrooms: Preheat the oven to 250 degrees F.
Put the olive oil, pink peppercorns, paprika, salt, garlic, bay leaves, rosemary and thyme in a pot and heat until simmering. Put the mushrooms in an oven-safe casserole dish or pan and cover them with the simmering oil mixture from the pot. Bake for about 30 minutes. Keep warm until serving.
For the potato puree: Put the potatoes in a large pot and cover well with cold salted water. Bring to a boil, lower the temperature to medium and simmer until cooked, 15 to 20 minutes.
While the potatoes are cooking, put the milk in a small pot and warm over low heat; keep warm.
Drain the potatoes in a colander and let them sit for a minute or two to make sure all the water is drained out. Put the potatoes through a potato ricer or food mill, transferring them back to the same pot you boiled them in. (If you do not have a ricer or food mill, you can put the potatoes back into the same pot and mash them well with a potato masher or beat them to a mash with a wooden spoon.)
Put the pot over low heat and begin incorporating the butter a little at a time. When you have added a quarter of the butter, add a little of the warm milk to help maintain an emulsion. Repeat these steps until all of the butter is incorporated into the puree. Season with salt and pepper.
To plate, place about a cup of the potato puree into each bowl. Place a spoonful of the mushrooms in the center of the puree and top with the crisped guanciale. Sprinkle the toasted pine nuts around the bowl and drizzle the beef jus (or demi glace) and a little of the mushroom oil sporadically around the dish. Top with a little of the chopped chives if using for an added touch.
The preserved mushrooms can also be made ahead and refrigerated, after cooling, in jars or a plastic container, covered with the flavored oil. Reheat in a low oven or for about 10 seconds in the microwave before using.
This recipe was provided by a chef, restaurant or culinary professional. It has not been tested for home use.