Trim hard fat from the chuck roast and cut into 1-inch cubes. Pat very dry with paper towels.
Dice the celery, carrots, and onion into small even pieces and mince the garlic. Chop the parsley and grate the Parmesan, then refrigerate both for the end.
Rinse the lentils under cold running water in a fine mesh strainer and pick out any small stones or debris. Measure out the broth, herbs, and bay leaves.
Heat the olive oil in a Dutch oven over medium high heat for about 2 minutes until it shimmers. Season the beef with salt and pepper.
Add the beef in a single layer, working in two batches if needed so the pot is not crowded. Brown undisturbed for 2 minutes, then turn and continue for about 8 minutes total until deeply golden on most sides. Transfer to a plate.
Reduce heat to medium and add the celery, carrots, and onion to the same pot. Cook for about 8 minutes, stirring often, until the onion is soft and translucent, scraping up the browned bits.
Stir in the garlic, oregano, thyme, and bay leaves. Cook for 1 minute just until the garlic smells fragrant, so it does not burn.
Pour in the beef broth and diced tomatoes with their juices. Return the browned beef and any collected juices to the pot and bring to a boil over high heat.
Reduce heat to medium low, cover, and simmer for 1 hour, stirring every 15 minutes or so. Skim off any foam and check that the beef is just beginning to turn tender.
Stir the rinsed lentils into the soup, making sure they are fully submerged. Cover and simmer for 35 to 40 minutes, stirring now and then, until the lentils are tender but still hold their shape and the beef pulls apart easily.
If the soup is too thick, stir in 1/2 to 1 cup of water or extra broth to loosen it.
Remove and discard the bay leaves. Taste and add more salt and pepper as needed, remembering the Parmesan will add saltiness. Stir in the parsley and rest off the heat for 5 minutes.
Ladle into warm bowls, making sure each serving gets plenty of beef and lentils. Sprinkle each bowl with freshly grated Parmigiano Reggiano and serve right away.