Heat a Dutch oven over medium high heat. Sauté the guanciale pieces without any oil until some of the fat has rendered and they turn golden brown. Remove and set aside.
Trim and cut your beef chuck into chunks. Dab with paper towels. Set aside and allow to come to room temperature before browning. Meanwhile, mix three tablespoons of all-purpose flour with salt and pepper. If your pan is dry, add a couple of tablespoons of vegetable oil. Brown the chunks of beef in batches so that each side can achieve a nice golden-brown crust. If there are too many pieces of beef in the pan, they won’t brown. Remove from the pan.
Prepare an ice bath to blanch your pearl onions.
At this point, if your pan is too dry, add another tablespoon of vegetable oil. Sauté the carrots and onions in the oil until the onions are soft and translucent, about five minutes. Then, add in the minced garlic, tomato paste, guanciale, and brown beef chunks. Deglaze the pan with the red wine. Allow to cook for a few minutes to cook the alcohol out of the wine. Add in the beef stock, herbs, and demi-glace before dropping the heat to medium low. Do not cover as you will need to cook out a lot of moisture. Simmer for one hour.
While your stew is cooking, bring a small sauce pot of water to a boil. Blanch the pearl onions in the boiling water for one minute. Drop into the ice bath. Using a pairing knife, slip the small onions out of their skins. Sauté the pearl onions in a couple of tablespoons of unsalted butter until they have achieved some color. Repeat with the halved button mushrooms. Add both to the stew as they are ready.
Fifteen minutes before the stew is ready, take three tablespoons of the softened butter and mix with one tablespoon of all-purpose flour to make a beurre manié. This mixture will help thicken up your stew in the last stretch of cooking.
Remove the thyme branches and bay leaves before serving. Top the plated stew with chopped parsley and enjoy with your starch of choice!
