Heat a large pot over medium heat. Cook and stir sausage until browned, about 5 minutes. Add kale stems, carrots, and onion; saute until soft, about 5 minutes. Pour in water and lentils; bring to a boil. Reduce heat to a simmer until lentils are tender, about 20 minutes.

Stir tomato paste, vinegar, brown sugar, garlic powder, garam masala, thyme, dill, tarragon, and salt into the pot. Return to a boil. Reduce heat; simmer, uncovered, until flavors blend, about 15 minutes. Toss in kale leaves and let wilt, about 5 minutes.