Special equipment: 2 large pieces of cheesecloth and kitchen twine
Preheat the oven to 300 degrees F.
In a Dutch oven, cook the bacon over medium-high heat until crisp; remove to a plate with a slotted spoon, leaving the fat in the pot. Season the beef with salt and pepper. Working in batches, place the beef in the pot in a single layer, sear until dark brown on all sides and remove to a plate. Reserve the fat in the pot.
Place the pot over medium heat and whisk the flour into the reserved fat. Slowly whisk in the beef broth and bring to a simmer, stirring frequently, until thickened, 3 to 5 minutes. Return the beef and bacon to the pot.
Cut 2 large pieces of cheesecloth and lay them on a clean work surface to form a cross. Pile the onion, carrots, garlic cloves, thyme, bay leaves, peppercorns and 10 parsley sprigs in the center. Gather the ends together to form a bundle and tie closed with kitchen twine. Place in the pot.
Add the wine and tomato paste to the pot, cover and transfer to the oven. Cook until the beef is tender, about 2 1/2 hours. Remove and discard the cheesecloth bundle. Remove the beef to a plate. Bring the remaining liquid in the pot to a boil and cook until reduced by half, about 10 minutes. Reduce the heat to low and return the beef to the pot. Add the pearl onions.
Melt the butter in a large skillet over medium heat. Add the mushrooms and saute until browned, about 5 minutes. Transfer to the pot. Garnish with the chopped parsley and serve.