Hearty and rustic French lentilsor lentils du Puyare smaller and darker than regular brown lentils and hold their shape better during cooking. Look for them at specialty or natural food stores or online. If French lentils aren't available, brown lentils will work just as well.
In a Dutch oven bring broth and the water to boiling. Add lentils; return to boiling. Reduce heat. Cover and simmer for 15 minutes.
Meanwhile, in a large skillet cook mushrooms, carrots, and leeks in hot oil over medium heat about 5 minutes or until leeks are tender. Stir mushroom mixture, kale, salt, and pepper into the lentil mixture. Bring to boiling; reduce heat. Simmer covered, about 15 minutes or until lentils are tender. Stir in drained tomatoes; heat through.
Ladle soup into bowls. Top soup in each bowl with a spoonful of pesto.