Preheat the oven to 325 degrees Fahrenheit
Pat dry the beef pieces with paper towels. Place the beef in a large bowl and season with salt and pepper. Add the flour and toss to coat. (see notes)
In a large Dutch oven or large heavy pot, heat 2 tablespoon of olive oil over medium-high heat. When the oil is hot, sear the beef for 4-5 minutes or until golden brown on all sides (you will have to sear the meat in batches, not to overcrowd the pot). Transfer the seared meat to a plate and set aside. Add the remaining oil and continue searing the meat until all the beef is browned. Add additional oil, if needed.
Lower the heat to medium and stir in the onions and carrots. Sauté stirring often until the onions become translucent, about 4-5 minutes. Add the garlic and sauté for about a minute.
Add the red wine and bring to a boil scrapping the bottom of the pan to release the brown bits. Cook for about 5 minutes, then stir in the tomato paste and return the beef to the pot with any collected juices. Stir in broth, adding enough to cover the meat. Stir in the thyme and bay leaves. Bring to a boil.
Cover the pot or Dutch oven and transfer to the oven. Cook until the meat becomes tender, about 1 1/4 hour to 1 1/2 hours. Remove from the oven. Season to taste with salt and black pepper.
In a medium sauté pan over medium heat, melt the butter. Add the mushrooms and sauté for about 8 minutes or until the mushrooms are lightly browned. Remove from the heat.
Stir in mushrooms, pearl onions and frozen peas to the stew. If the stew is too thick, add additional broth until the gravy reaches your desired consistency. Return the pot to the oven and cook, covered for an additional 15 minutes.
Remove from the oven and adjust seasoning. Discard bay leaves and garnish with chopped parsley. Serve.