Heat a large, wide saucepan over medium heat. Add oil, then sausages. Turn sausages occasionally until they lose their pink colour, 4 to 6 minutes. Remove to a plate. Add onion, leek, carrots and garlic to pan. Cook until onion starts to soften, about 3 minutes. meanwhile, thinly slice sausages. Stir in tomato paste, coriander, salt, sausages and any juices. Continue to cook, stirring frequently, until flavour develops, 5 more minutes. Pour in 4 cups water. Bring to a boil. Stir in kale and reduce heat to medium. Cover and gently boil, stirring occasionally, until kale is tender, 5 to 7 minutes. Stir in lentils. If soup is too thick, stir in more water. Ladle soup into bowls. Sprinkle with parmesan. Serve immediately.