Preheat an oven to 350°F. Place the beef in a bowl, sprinkle with the flour and toss together.
In a large Dutch oven over medium heat, warm 1 Tbs. of the olive oil. Add the onion and sauté until the onion
soft, about 10 minutes. Using a slotted spoon, transfer to a plate. Increase the heat to medium-high and add the remaining 1 Tbs. oil. Working in batches, add the beef and cook, turning occasionally, until golden brown on all sides, 10 to 15 minutes.
Using kitchen string, tie the parsley and thyme sprigs and bay leaves into a bundle. Return the onion to the pan along with the herb bundle and the garlic. Increase the heat to high and pour in the wine. Bring to a boil, stirring to scrape up any browned bits from the pan bottom, and boil until the wine is reduced by half, about 5 minutes. Add the broth and tomato paste and bring to a boil. Cover, place in the oven and cook until the beef can be easily pierced with a knife, about 1 1/2 hours.
Meanwhile, in a saucepan, combine the pearl onions with water to cover. Bring to a boil and boil for 2 minutes. Drain, rinse and drain again. Trim off the root end of each onion, then cut a shallow X in each trimmed end. Squeeze each onion gently to slip off the skin. set aside.
In a frying pan over medium-high heat, melt 1 Tbs. schmaltz. Add the mushrooms and cook, stirring occasionally, until lightly golden, about 10 minutes. Transfer to a plate. Melt the remaining 1 Tbs. schmaltz in the same pan. Add the pearl onions and cook over medium heat, stirring occasionally, until lightly golden, about 10 minutes. set aside.
When the beef is tender, remove it from the oven and add the onions. Place over medium heat and bring to a simmer. Cook, uncovered, until the onions are tender, about 20 minutes. Add the mushrooms and stir to heat through. Discard the herb bundle. Stir in the chopped parsley and season with salt and pepper.