Heat olive oil in a large pot over medium heat. Add the onion and carrots. Cook until they soften, about 10 minutes.
Add garlic, paprika, and cumin, and cook for 2 more minutes, or until the spices become fragrant.
Add the lentils, vegetable broth, potatoes, and salt to the pot. Turn the heat to high to bring it to a boil, then reduce the heat to a simmer. Cover and cook for 20 or until the lentils are soft, stirring occasionally.
Add the chopped kale and coconut milk. Stir and cook for 2 minutes.