In a large soup pot, heat olive oil. Add onion and saute until fragrant, about 3-4 minutes. Add carrot and celery and cook for a few more minutes, uncovered, until vegetables begin to soften.
Add lentils and tomato paste to vegetable mixture and stir. Add broth or water and stir to combine. Add a pinch of salt, and bring to a simmer. Simmer partially covered for 40 minutes, until the lentils are soft.
Ten minutes before the soup is done, soften the kale in a pot of salted boiling water for 5 minutes. Rinse, drain, and set aside.
To serve, add a healthy ladleful of lentil soup to a bowl. Top with a spoonful of kale and a dollop of yogurt or sour cream.