This classic French dish is a concoction of beef slowlysteeped in Burgundy wine that is at once seductive and -- since it's a simple stew at heart -- laid-back.
Cut two 12-by-22-inch pieces of cheese-cloth; lay them on a clean work surface, overlapping each other perpendicularly in the center to form a cross. Pile the chopped onion, carrots, garlic cloves, parsley sprigs, thyme, rosemary, bay leaves, and peppercorns in the center.
Gather the ends together to enclose contents completely, and tie the top with kitchen twine. Place in an 8-quart Dutch oven, and set aside.
Preheat oven to 300 degrees. Heat oil in a large skillet over medium heat. Add salt pork, and saute until brown and crisp, about 7 minutes. Using a slotted spoon, transfer pork to Dutch oven, leaving rendered fat in skillet.
Season beef cubes with salt and pepper. Working in two batches, place beef in skillet in a single layer; cook until dark brown on all sides, about 6 minutes total.
Using tongs, transfer beef to Dutch oven, reserving fat in skillet.
Whisk the flour into fat in the skillet. Slowly whisk in beef stock, and bring to a simmer over medium heat, stirring frequently until thickened.
Pour mixture into Dutch oven around cheesecloth bundle. Add wine and tomato paste, and season with salt and pepper; stir to combine. Bring to a boil over high heat. Cover; transfer to oven. Cook until beef is very tender, about 2 1/2 hours.
Remove pot from oven, and transfer cheesecloth bundle to a large sieve set over a bowl. With a wooden spoon, press on bundle to release as much liquid as possible. Discard bundle, and pour accumulated juices into Dutch oven.
Remove beef and pork from Dutch oven; reserve. Return liquid to a boil over high heat; reduce to 4 cups, about 10 minutes. Skim surface as needed with a large metal spoon. Reduce heat to low; return beef and pork to Dutch oven.
While sauce is reducing further, set the skillet over high heat. Add the pearl onions, the water, butter, sugar, and a large pinch of salt. Bring to a boil, and reduce heat to medium; simmer until almost all the liquid evaporates, 5 to 8 minutes. Raise heat to medium-high, and add the mushrooms. Cook, stirring occasionally, until vegetables are browned and glazed, about 5 minutes. Remove from heat. Transfer contents to Dutch oven, and simmer over medium heat until heated through. Adjust seasoning with salt and pepper as desired, and serve at once. Garnish each serving with chopped parsley.