Heat 2 tablespoons of olive oil in a large Dutch oven over medium-high heat. Add the beef chuck cubes to sear each side until golden brown, about 4–5 minutes per side. Remove the beef and set aside.

In the same pot, add the chopped onions and sauté for about 5 minutes until golden. Add minced garlic and cook for 1 minute.

Toss sliced carrots into the pot and cook for 2–3 minutes. Stir in the tomato paste, cooking for an additional minute.

Sprinkle all-purpose flour over the vegetables. Stir to coat and pour in beef stock while stirring. Add water and bring to a simmer. Return the browned beef to the pot.

Add thyme, bay leaf, salt, and pepper. Stir, cover, and simmer gently for 2½ to 3 hours.

Heat another tablespoon of olive oil in a skillet over medium heat. Add sliced mushrooms and sauté for 5-7 minutes. Toss in pearl onions and cook for another 3-4 minutes.

Once beef is tender, stir the sautéed mushrooms and pearl onions into the pot and simmer for another 10 minutes.