Start by prepping your ingredients. Trim the beef cheeks of excess fat and cut them into large chunks. Chop your vegetables; ensure that the carrots and celery are in manageable sizes. This helps them cook evenly.

In a large, heavy-bottomed pot, add a drizzle of extra virgin olive oil. Heat it over medium-high. Once the oil shimmers, toss in the beef pieces, making sure not to crowd the pan.

Remove the beef from the pot and set it aside. In the same pot, add the pancetta. Cook it for 4-5 minutes until crispy. This adds a delightful smokiness to the dish.

Next, add the quartered onion, smashed garlic, chopped carrots, and celery to the pot. Cook for about 5 minutes until they start to soften. The soaking up of fat from the pancetta gives them a lovely flavor.

Sprinkle the plain flour over the vegetables. Stir well to coat everything evenly. This will help thicken the sauce later on. Cook for another 2 minutes to ensure the flour cooks out its raw taste.

Return the browned beef to the pot, and mix well. It should look delightful already! Now, pour in the Burgundy wine. Stir gently to combine and scrape any brown bits from the bottom of the pot. These are treasure troves of flavor!

Throw in the halved mushrooms, shallots, bay leaves, balsamic vinegar, thyme, mustard, and allspice. Stir it again; it should look colorful, comforting, and ready to simmer.

Bring the mixture to a gentle simmer, cover, and reduce the heat to low. Let it cook for 3 to 4 hours, stirring occasionally. The low heat allows the flavors to meld together beautifully, and the beef will become fork-tender.

When the time is up, taste the stew. Add salt and pepper to taste if needed. A sprinkle of fresh flat-leaf parsley right before serving adds a lovely burst of color.