Heat the olive oil in a large pot over medium heat. Add the ground beef and cook until browned, breaking it up with a spoon as it cooks.
Add the diced onion, carrots, and minced garlic to the pot. Cook for 3 to 4 minutes until the vegetables begin to soften.
Stir in the rinsed lentils, beef broth, diced tomatoes, oregano, paprika, salt, and pepper. Bring the mixture to a boil.
Reduce the heat to low, cover the pot, and simmer for 25 to 30 minutes until the lentils are tender.
Turn off the heat and stir in the fresh spinach until it wilts.