Heat a large pot over medium heat and add the ground beef, onion, and garlic. Cook until the beef is browned and the onion is soft, breaking up the meat as it cooks.
Stir in the carrots, lentils, beef broth, diced tomatoes, oregano, salt, and pepper. Bring the mixture to a boil.
Reduce the heat to low, cover the pot, and simmer for 35 minutes until the lentils and carrots are tender.
Turn off the heat and stir in the spinach until it wilts into the stew.