Pat the beef cubes dry with paper towels and season generously with salt and freshly ground black pepper.
Heat 2 tablespoons of olive oil in a large heavy-bottomed pot or Dutch oven over medium-high heat.
Working in batches, sear the beef cubes until browned on all sides, about 4-5 minutes per batch. Transfer the browned beef to a plate and set aside.
Add the remaining 1 tablespoon of olive oil to the pot. Add the pearl onions and carrots, and sauté for 5 minutes until they begin to soften.
Add the mushrooms and continue to cook for another 5 minutes until they release their moisture and start to brown.
Stir in the minced garlic and tomato paste, cooking for 1 minute until fragrant.
Return the browned beef to the pot. Sprinkle the flour over the ingredients and stir well to coat everything evenly. Cook for 2 minutes to remove the raw flour taste.
Pour in the beef broth and water, scraping the bottom of the pot to release any browned bits.
Add the Worcestershire sauce, fresh thyme leaves, and bay leaf. Stir to combine.
Bring the mixture to a gentle simmer, then reduce the heat to low. Cover the pot with a lid and cook for 2 to 2 1/2 hours, stirring occasionally, until the beef is very tender.
Remove the lid during the last 15 minutes of cooking to allow the sauce to thicken slightly.
Discard the bay leaf. Stir in the unsalted butter until melted and incorporated to give the sauce a glossy finish.
Taste and adjust seasoning with salt and pepper if needed.
Sprinkle with chopped fresh parsley before serving.