Blot every surface of the beef with paper towels, then distribute salt and black pepper over the pieces. The cubes should look dry rather than slick with moisture.
Warm the olive oil in a large pot over medium heat, then brown an uncrowded batch of beef for about 3 minutes on each side. Listen for a steady sizzle and look for a golden crust before turning each piece.
Transfer the browned cubes to a plate and continue with the remaining beef, adding oil as necessary. The pot should collect brown cooking residue without developing black, scorched patches.
Cook the sliced mushrooms in the same pot for 5 minutes. Look for golden surfaces and crisp edges as their released moisture cooks away.
Stir in the onion, carrot, and celery and cook for 5 minutes. The onion should lose its raw firmness, and the vegetables should begin to soften.
Add the garlic for 1 minute, then mix in the tomato paste until it coats the vegetables. The garlic should smell fragrant, and the paste should leave the vegetables evenly red.
Pour in the broth, add the thyme and rosemary, return the beef to the pot, and season with 1/2 teaspoon salt and black pepper. The liquid will loosen the browned residue and take on a deeper savory color.
Bring the liquid to a boil, lower the heat to a gentle simmer, and cook for 50 minutes to an hour, until the beef is tender. A finished cube should yield easily when you press and twist a fork into it.