Prepare the Base: Heat olive oil in a Dutch oven over medium heat. Sauté the onion, carrots, and celery until softened (about 5 minutes). Add garlic and cook for 1 minute.
Build the Soup: Stir in the diced tomatoes, lentils, broth, and seasonings. Bring to a boil, then reduce to a simmer. Stir occasionally to prevent the lentils from sticking to the pot. Cover and cook for 25 minutes.
Add the Rice: Stir in the rice and greens. Simmer for another 20 minutes until the rice is al dente and the lentils are tender. Adjust seasoning as needed.
Serve: Ladle into bowls and garnish with fresh parsley or a drizzle of olive oil.